＜IUT国際会議 2つのシリーズ＞ 1． http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/IUT-schedule.html RIMS Promenade in Inter-Universal Teichmuller Theory Org.: Collas (RIMS); Debes, Fresse (Lille). The seminar takes place every two weeks on Thursday for 2 hours by Zoom 17:30-19:30, JP time (9:30-11:30, UK time; 10:30-12:30 FR time) ? we refer to the Programme for descriptions of the talks and associated references. http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/documents/RIMS-Lille%20-%20Promenade%20in%20Inter-Universal%20Teichm%C3%BCller%20Theory.pdf
つづき （参考） 関連： 望月新一（数理研） http://www.kurims.kyoto-u.ac.jp/~motizuki/ News - Ivan Fesenko https://www.maths.nottingham.ac.uk/plp/pmzibf/nov.html Explicit estimates in inter-universal Teichmuller theory, by S. Mochizuki, I. Fesenko, Y. Hoshi, A. Minamide, W. Porowski, RIMS preprint in November 2020, updated in June 2021, accepted for publication in September 2021 https://ivanfesenko.org/wp-content/uploads/2021/11/Explicit-estimates-in-IUT.pdf NEW!! (2020-11-30) いわゆる南出論文（5人論文） より P4 Theorem A. (Effective versions of ABC/Szpiro inequalities over mono-complex number fields) Theorem B. (Effective version of a conjecture of Szpiro) Corollary C. (Application to “Fermat’s Last Theorem”) P56 Corollary 5.9. (Application to a generalized version of “Fermat’s Last Theorem”) Let l, m, n be positive integers such that min{l, m, n} > max{2.453 ・ 10^30, log2 ||rst||C, 10 + 5 log2(rad(rst))}. Then there does not exist any triple (x, y, z) ∈ S of coprime [i.e., the set of prime numbers which divide x, y, and z is empty] integers that satisfies the equation
http://www.kurims.kyoto-u.ac.jp/~motizuki/Essential%20Logical%20Structure%20of%20Inter-universal%20Teichmuller%20Theory.pdf ＜PRIMS出版記念論文＞ [9] On the Essential Logical Structure of Inter-universal Teichmuller Theory in Terms of Logical AND "∧"/ Logical OR "∨" Relations: Report on the Occasion of the Publication of the Four Main Papers on Inter-universal Teichmuller Theory. PDF NEW!! (2021-03-06)
新一の「心の一票」 - 楽天ブログ shinichi0329/ （URLが通らないので検索たのむ） math jin：（IUTT情報サイト）ツイッター math_jin （URLが通らないので検索たのむ）
https://www.math.arizona.edu/~kirti/ から Recent Research へ入る Kirti Joshi Recent Research論文集 新論文（IUTに着想を得た新理論） https://arxiv.org/pdf/2106.11452.pdf Construction of Arithmetic Teichmuller Spaces and some applications Preliminary version for comments Kirti Joshi June 23, 2021
https://www.uvm.edu/~tdupuy/papers.html [ Taylor Dupuy's Homepage] 論文集 なお、（メモ）TAYLOR DUPUYは、arxiv投稿で [SS17]を潰した（下記） https://arxiv.org/pdf/2004.13108.pdf PROBABILISTIC SZPIRO, BABY SZPIRO, AND EXPLICIT SZPIRO FROM MOCHIZUKI’S COROLLARY 3.12 TAYLOR DUPUY AND ANTON HILADO Date: April 30, 2020. P14 Remark 3.8.3. (1) The assertion of [SS17, pg 10] is that (3.3) is the only relation between the q-pilot and Θ-pilot degrees. The assertion of [Moc18, C14] is that [SS17, pg 10] is not what occurs in [Moc15a]. The reasoning of [SS17, pg 10] is something like what follows:
P15 (2) We would like to point out that the diagram on page 10 of [SS17] is very similar to the diagram on §8.4 part 7, page 76 of the unpublished manuscript [Tan18] which Scholze and Stix were reading while preparing [SS17]. References [SS17] Peter Scholze and Jakob Stix, Why abc is still a conjecture., 2017. 1, 1, 1e, 2, 7.5.3 ( https://www.math.uni-bonn.de/people/scholze/WhyABCisStillaConjecture.pdf Date: July 16, 2018. https://ncatlab.org/nlab/files/why_abc_is_still_a_conjecture.pdf Date: August 23, 2018. ) [Tan18] Fucheng Tan, Note on IUT, 2018. 1, 2
なお "[SS17] Peter Scholze and Jakob Stix, Why abc is still a conjecture., 2017."は、2018の気がする ”[Tan18] Fucheng Tan, Note on IUT, 2018. 1, 2”が見つからない。”the unpublished manuscript [Tan18]”とはあるのだが（＾＾ 代わりに、ヒットした下記でも、どぞ （2018の何月かが不明だが、2018.3のSS以降かも）
http://www.kurims.kyoto-u.ac.jp/~motizuki/Tan%20---%20Introduction%20to%20inter-universal%20Teichmuller%20theory%20(slides).pdf Introduction to Inter-universal Teichm¨uller theory Fucheng Tan RIMS, Kyoto University 2018 To my limited experiences, the following seem to be an option for people who wish to get to know IUT without spending too much time on all the details. ・ Regard the anabelian results and the general theory of Frobenioids as blackbox. ・ Proceed to read Sections 1, 2 of [EtTh], which is the basis of IUT. ・ Read [IUT-I] and [IUT-II] (briefly), so as to know the basic definitions. ・ Read [IUT-III] carefully. To make sense of the various definitions/constructions in the second half of [IUT-III], one needs all the previous definitions/results. ・ The results in [IUT-IV] were in fact discovered first. Section 1 of [IUT-IV] allows one to see the construction in [IUT-III] in a rather concrete way, hence can be read together with [IUT-III], or even before. S. Mochizuki, The ´etale theta function and its Frobenioid-theoretic manifestations. S. Mochizuki, Inter-universal Teichm¨uller Theory I, II, III, IV.
http://www.kurims.kyoto-u.ac.jp/daigakuin/Tan.pdf 教員名: 譚 福成（Tan, Fucheng） P-adic Hodge theory plays an essential role in Mochizuki's proof of Grothendieck's Anabelian Conjecture. Recently, I have been studying anabeian geometry and Mochizuki's Inter-universal Teichmuller theory, which is in certain sense a global simulation of p-adic comparison theorem.
コピーペースト下記 Here are some relations between the three generalisations of CFT and their further developments:
2dLC?－－ 2dAAG－－－ IUT l ／ ｜ ｜ l ／ ｜ ｜ l／ ｜ ｜ LC 2dCFT anabelian geometry ＼ ｜ ／ ＼ ｜ ／ ＼ ｜ ／ CFT 注）記号： Class Field Theory (CFT), Langlands correspondences (LC), 2dAAG = 2d adelic analysis and geometry, two-dimensional (2d) (P8 "These generalisations use fundamental groups: the etale fundamental group in anabelian geometry, representations of the etale fundamental group (thus, forgetting something very essential about the full fundamental group) in Langlands correspondences and the (abelian) motivic A1 fundamental group (i.e. Milnor K2) in two-dimensional (2d) higher class field theory.") https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/documents/Fesenko%20-%20IUT%20and%20modern%20number%20theory.pdf Fesenko IUT and modern number theory つづく
（IUTに対する批判的レビュー） https://zbmath.org/07317908 https://zbmath.org/pdf/07317908.pdf Mochizuki, Shinichi Inter-universal Teichmuller theory. I: Construction of Hodge theaters. (English) Zbl 07317908 Publ. Res. Inst. Math. Sci. 57, No. 1-2, 3-207 (2021). Reviewer: Peter Scholze (Bonn)
BuzzardのICM22講演原稿 Inter-universal geometry とABC 予想47 http://2chb.net/r/math/1635332056/84 84 名前：38[] 投稿日：2021/12/23(木) 19:42:33.42 ID:iz9G4jw+ [1/2] Buzzardの原稿が出たヨ！ https://arxiv.org/abs/2112.11598 >A great example is Mochizuki’s claimed proof of the ABC conjecture [Moc21]. >This proof has now been published in a serious research journal, however >it is clear that it is not accepted by the mathematical community in general.
86 名前：１３２人目の素数さん[] 投稿日：2021/12/23(木) 20:46:56.21 ID:a0F2ZqKI >>84 ホントに出ていたね。その引用部分の少し後に次のことが書かれている。 Furthermore, the key sticking point right now is that the unbelievers argue that more details are needed in the proof of Corollary 3.12 in the main paper, and the state of the art right now is simply that one cannot begin to formalise this corollary without access to these details in some form (for example a paper proof containing far more information about the argument) (引用終り)
”Comments: 28 pages, companion paper to ICM 2022 talk”と明記もあるね 思うに、その意図は、「反論あるなら言ってきてね。反論の機会を与える。反論なき場合はこのまま総会発表とする」ってことか （西洋流で、「黙っていたから 認めたってことじゃん」みたいなｗ） 普通は、こんな形でプレプリ出さない気がするな さあ、面白くなってきたかも ドンパチ派手にやってほしい
https://www.math.columbia.edu/~woit/wordpress/?p=12775 Not Even Wrong Various and Sundry Posted on April 18, 2022 by woit Last week a review of the Mochizuki IUT papers appeared at Math Reviews, written by Mohamed Saidi. His discussion of the critical part of the proof is limited to: Theorem 3.11 in Part III is somehow reinterpreted in Corollary 3.12 of the same paper in a way that relates to the kind of diophantine inequalities one wishes to prove. One constructs certain arithmetic line bundles of interest within each theatre, a theta version and a q-version (which at the places of bad reduction arises essentially from the q-parameter of the corresponding Tate curve), which give rise to certain theta and q-objects in certain (products of) Frobenioids: the theta and q-pilots. By construction the theta pilot maps to the q-pilot via the horizontal link in the log-theta lattice. One can then proceed and compare the log-volumes of the images of these two objects in the relevant objects constructed via the multiradial algorithm in Theorem 3.11.
Saidi gives no indication that any one has ever raised any issues about the proof of Corollary 3.12, with no mention at all of the detailed Scholze/Stix criticism that this argument is incorrect. In particular, in his Zentralblatt review Scholze writes:
Unfortunately, the argument given for Corollary 3.12 is not a proof, and the theory built in these papers is clearly insufficient to prove the ABC conjecture…. In any case, at some point in the proof of Corollary 3.12, things are so obfuscated that it is completely unclear whether some object refers to the q-values or the -values, as it is somehow claimed to be definitionally equal to both of them, up to some blurring of course, and hence you get the desired result.
After the Saidi review appeared, I gather that an intervention with the Math Reviews editors was staged, leading to the addition at the end of the review of
Editor’s note: For an alternative review of the IUT papers, in particular a critique of the key Corollary 3.12 in Part III, we refer the reader to the review by Scholze in zbMATH: https://zbmath.org/1465.14002.
Since the early days of people trying to understand the claimed proof, Mochizuki has pointed to Saidi as an example of someone who has understood and vouched for the proof (see here). Saidi is undoubtedly well aware of the Scholze argument and his decision not to mention it in the review makes clear that he has no counter-argument. The current state of affairs with the Mochizuki proof is that no one who claims to understand the proof of Corollary 3.12 can provide a counter-argument to Scholze. Saidi tries to deal with this by pretending the Scholze argument doesn’t exist, while Mochizuki’s (and Fesenko’s) approach has been to argue that Scholze should be ignored since he’s an incompetent. The editors at PRIMS claim that referees have considered the argument, but say they can’t make anything public. This situation makes very clear that there currently is no proof of abc.
つづき ＜再録＞ 応援スレ53 http://2chb.net/r/math/1615164505/492 Preface to the Special Issue Volume 57, Issue 1/2, 2021 PRIMS It is our great pleasure to publish a special issue of Publications of the Research Institute for Mathematical Sciences (PRIMS) for Inter-universal Teichm ̈uller Theory, I–IV by Shinichi Mochizuki. There are two main reasons for publishing this series of papers in a special issue. One is their volume and importance. The other is to avoid the conflict of interest that arises because the author is Editor-in-Chief of PRIMS. As a general rule, when a paper is submitted to PRIMS by a member of the Editorial Board, the member should be entirely excluded from the editorial committee charged with handling it. When Mochizuki became Editor-in-Chief of PRIMS in April 2012, the Editorial Board further decided that, in the case of his submission, they would form a special committee to handle it, excluding him and with an Editor-in-Chief substituting for him. When he submitted the present series of papers on August 30, 2012, Akio Tamagawa took the job of Editor-in-Chief of the special committee. Masaki Kashiwara later joined the committee, and he and Tamagawa served as co-Editors-in-Chief. Several mathematicians kindly accepted an invitation to referee the papers; we are extremely grateful to them for their efforts and patience. Based on their reports, we had numerous editorial meetings. In particular because of the total length of the series of papers, it took a long time for the Editorial Committee to arrive at the final decision of acceptance.
Editorial Committee for the Special Issue Editors-in-Chief Masaki Kashiwara, Akio Tamagawa Other Members Tomoyuki Arakawa, Masahito Hasegawa, Takashi Kumagai, Kazuhisa Makino, Takuro Mochizuki, Shigeru Mukai, Hiraku Nakajima, Kenji Nakanishi, Tomotada Ohtsuki, Kaoru Ono, Narutaka Ozawa, Michio Yamada (引用終り) こんなところで
The present paper is the first in a series of four papers, the goal of which is to establish an arithmetic version of Teichmuller theory for number fields equipped with an elliptic curve ? which we refer to as "inter-universal Teichmuller theory" ? by applying the theory of semi-graphs of anabelioids,
Frobenioids, the etale theta function, and log-shells developed in earlier papers by the author. We begin by fixing what we call "initial Θ-data", which consists of an elliptic curve EF over a number field FF, and a prime number l?5l?5, as well as some other technical data satisfying certain technical properties. This data determines various hyperbolic orbicurves that are related via finite etale coverings to the once-punctured elliptic curve XF determined by EF. These finite etale coverings admit various symmetry properties arising from the additive and multiplicative structures on the ring Fl=Z/lZ acting on the ll-torsion points of the elliptic curve. We then construct "Θ±ellNF-Hodge theaters" associated to the given Θ- data. These Θ±ellNF-Hodge theaters may be thought of as miniature models of conventional scheme theory in which the two underlying combinatorial dimensions of a number field ? which may be thought of as corresponding to the additive and multiplicative structures of a ring or, alternatively, to the group of units and value group of a local field associated to the number field ? are, in some sense, "dismantled" or "disentangled" from one another.
All Θ±ellNF-Hodge theaters are isomorphic to one another, but may also be related to one another by means of a "Θ-link", which relates certain Frobenioid-theoretic portions of one Θ±ellNF-Hodge theater to another in a fashion that is not compatible with the respective conventional ring/scheme theory structures. In particular, it is a highly nontrivial problem to relate the ring structures on either side of the Θ-link to one another. This will be achieved, up to certain "relatively mild indeterminacies", in future papers in the series by applying the absolute anabelian geometry developed in earlier papers by the author. The resulting description of an "alien ring structure" [associated, say, to the domain of the Θ-link] in terms of a given ring structure [associated, say, to the codomain of the Θ-link] will be applied in the final paper of the series to obtain results in diophantine geometry. Finally, we discuss certain technical results concerning profinite conjugates of decomposition and inertia groups in the tempered fundamental group of a pp-adic hyperbolic curve that will be of use in the development of the theory of the present series of papers, but are also of independent interest. (引用終り) 以上
Think you're poor? Think you're Free? Follow me, Follow me! Look up and see the Thinkers at your head Look up and Show the Mersey if you can Look up and see the sufferers of the street Look up, Look up, Upon your Fellow man! How do you do? My name's Ga腐゛roche. These are Math People. Here's Math patch. Not much to look at,nothing posh Nothing that you'd call up to scratch. This is Math school, Math high school Here in the school of Saint Math We live on crumbs of humble piety Tough on the Heart, but what the hell! Take your place, Take your chance, Viva la curve！ Viva la curve！
There was a time math killed the Aristotle. Mathematician tried to CHANGE THE WORLD TOO FAST. Now we have got another Think Aristotle is no better than the last. This is the think that fought for Liberty Now when we fight, we fight for brain. Here is the thing about equality. Everyone's equal when they're think. Take your place. Take your chance.
(講演タイトルに付与されているリンクをクリックすると講演スライドのファイルが得られます.) 9月5日(月) 11:00--12:30 : 山下(RIMS) Introduction 14:00--15:30 : 山下(RIMS) [CombGC] Part I 16:00--17:30 : 山下(RIMS) [CombGC] Part II
9月6日(火) 10:00--11:00 : 南出(RIMS) The injectivity portion of combinatorial cuspidalization for FC-admissible outer automorphisms I 11:30--12:30 : 南出(RIMS) The injectivity portion of combinatorial cuspidalization for FC-admissible outer automorphisms II 14:00--15:00 : 南出(RIMS) A combinatorial version of the Grothendieck Conjecture for outer representations of NN-type 15:30--16:30 : 南出(RIMS) The surjectivity portion of combinatorial cuspidalization for FC-admissible outer automorphisms 17:00--18:00 : 南出(RIMS) The Grothendieck-Teichmuller group as an open subgroup of the outer automorphism group of the etale fundamental group of a configuration space
>>150 9月7日(水) 9:00--10:30 : 飯島(広島大) F-admissibility and FC-admissibility Various operations on semi-graphs of anabelioids of PSC-type 11:00--12:30 : 飯島(広島大) Synchronization of cyclotomes 14:00--15:30 : 飯島(広島大) Profinite Dehn multi-twists Comparison with scheme theory 16:00--18:00 : 飯島(広島大) Centralizers of geometric monodromy
9月8日(木) 9:00--10:00 : 星(RIMS) Combinatorial Anabelian Geometry in the Absence of Group-theoretic Cuspidality 10:30--12:00 : 星(RIMS) Partial Combinatorial Cuspidalization for F-admissible Outomorphisms 13:30--14:20 : 星(RIMS) Synchronization of Tripods I 14:40--15:30 : 星(RIMS) Synchronization of Tripods II 16:00--16:50 : 星(RIMS) Glueability of Combinatorial Cuspidalizations I 17:10--18:00 : 星(RIMS) Glueability of Combinatorial Cuspidalizations II
9月9日(金) 9:00--10:30 : 辻村(RIMS) Combinatorial Belyi Cuspidalization 11:00--12:30 : 辻村(RIMS) Arithmetic Subquotients of the Grothendieck-Teichmuller Group 14:00--15:30 : 辻村(RIMS) Combinatorial Construction of the Field of Algebraic Numbers 16:00--18:15 : 辻村(RIMS) Combinatorial Construction of the Absolute Galois Group of the Field of Rational Numbers (引用終り) 以上
https://www.kurims.kyoto-u.ac.jp/~motizuki/travel-japanese.html 望月新一 出張・講演 [18] 宇宙際タイヒミューラー理論の論理構造 I, II, III （「代数的整数論とその周辺」 (Zoom) 2021年12月13日～14日） Lecture notes Lecture notes (marked up version for I, II, III) Classical roots of inter-universal Teichmuller theory Classical roots of inter-universal Teichmuller theory (marked up version) (引用終り) 以上
>>158 >望月新一 出張・講演 [18] 宇宙際タイヒミューラー理論の論理構造 I, II, III （「代数的整数論とその周辺」 (Zoom) 2021年12月13日～14日） > Lecture notes Lecture notes (marked up version for I, II, III) > Classical roots of inter-universal Teichmuller theory > Classical roots of inter-universal Teichmuller theory (marked up version)
さて AHGT？ google検索 "AHGT?" CNRS Lille University RIMS より
１） https://ahgt.math.cnrs.fr/ Arithmetic & Homotopic Galois Theory IRN Arithmetic & Homotopic Galois Theory The LPP-RIMS Arithmetic & Homotopic Galois Theory IRN (AHGT) is a CNRS France-Japan International Research Network between Lille University (Laboratoire de Mathematiques Paul Painleve), Ecole Normale Superieure - PSL (Departement de Mathematiques et Applications), and the Research Institute for Mathematical Sciences, Kyoto University.
AHGT News Dec 18, 2022 Ariane Mezard (ENS PSL) visits RIMS, Kyoto University, December 18, 2022 to January 18, 2023 Dec 7, 2022 Opening of the AHGT IRN website, see also ``France-RIMS collaboration: beyond the mathematical research frontier''. See also the news archives and the network activities. AHGT Seminar Dec 26, 2022 Deformations of p-adic Galois representations. Ariane Mezard (DMA, ENS Paris, France) For schedule and more, see the page of the AHGT seminar.
Arithmetic Homotopy Geometry Arithmetic Homotopy Geometry at RIMS -- seminars, workshops, talks -- in collaboration and with the support of my RIMS colleagues (esp. Prof. Tamagawa, Mochizuki, Hoshi,Tsujimura, Minamide, Sawada).
Personal interest in the moduli stacks of curves and its stack inertia stratification ? see for a glimpse; Includes simplical and homotopical algebraic geometry ? i.e. model categories and motivic considerations for stacks a la Morel-Voevodsky ?, the arithmetic geometry of curves ? e.g. G-covers, irreducible components of Hurwitz spaces, etale fundamental group ?, Grothendieck-Teichmuller theory ? e.g. mapping class groups, pants decompositions, Serre bonte ?, the arithmetic of operads ? in genus 0 via Friedlander etale topological type and prospaces, and the Tannakian formalism in Perverse sheaves.
Since 2023 this activity takes place in the CNRS France-Japan International Research Network LPP-RIMS ``Arithmetic & Homotopic Galois Theory'' (AHGT), see seminar and workshops, and publications.
Publications Talks Org. of Scientific Events (引用終り) 以上
下記 "Mar 6, 2023 Title [To be announced] by Noemie Combe, Max-Planck-Institut Leipzig, Germany." かな
https://ahgt.math.cnrs.fr/activities/ Arithmetic & Homotopic Galois Theory IRN Activities & Workshops The AHGT Seminar An hybrid seminar that takes place between LPP Lille and RIMS Kyoto on a monthly basis by Zoom.
Contact the local coordinator of your choice if you are interested.
Seminars of the Network RIMS Number Theory / Arithmetic Geometry Seminar (local) Lille Arithmetic and Topology Seminars Osaka Number theory Seminar Sorbonne-X ``Varietes Rationnelles'' Seminar Sorbonne Paris Nord ``Geometrie Arithmetique et Motivique'' Seminar ENS DMA ``Raconte-moi...'' Algebra and Geometry Seminar Next coming talks…
Dec 26, 2022 Deformations of p-adic Galois representations by Ariane Mezard, DMA, ENS Paris, France. Feb 6, 2023 Title [To be announced] by Speaker [TBD], Institute [TBD]. Mar 6, 2023 Title [To be announced] by Noemie Combe, Max-Planck-Institut Leipzig, Germany.
IRN？ これは >>203より Since 2023 this activity takes place in the CNRS France-Japan International Research Network LPP-RIMS ``Arithmetic & Homotopic Galois Theory'' (AHGT), この International Research Network →IRN でしょうか
>>204 >>今年3月に予定されている、AHGTの発足を記念する研究集会は、（私を含む）日仏の数論幾何学の研究者が一堂に会する重要な機会となる見込みです。 >"Mar 6, 2023 Title [To be announced] by Noemie Combe, Max-Planck-Institut Leipzig, Germany."
(参考) https://www.mathunion.org/icm/icm-2026 ICM 2026 International Congress of Mathematicians (ICM) 2026 in Philadelphia, USA | 22?29 July 2026 20th IMU General Assembly in New York City, USA | 19?20 July 2026 At its meeting in Helsinki, Finland, in July 2022, the 19th IMU General Assembly voted to accept the bid from the United States of America to host ICM 2026 and the 20th IMU General Assembly, with Philadelphia as venue for the ICM and New York City for the General Assembly.
ICM 2026 International Congress of Mathematicians (ICM) 2026 in Philadelphia, USA | 22?29 July 2026 20th IMU General Assembly in New York City, USA | 19?20 July 2026 At its meeting in Helsinki, Finland, in July 2022, the 19th IMU General Assembly voted to accept the bid from the United States of America to host ICM 2026 and the 20th IMU General Assembly, with Philadelphia as venue for the ICM and New York City for the General Assembly. Further information regarding ICM 2026 will be made available in due course.
The ICM Structure Committee for ICM 2026 Membership of the ICM Structure Committee for 2026 is as follows: Terence Tao [Chair] [email protected] Hiraku Nakajima [IMU President, ex officio] Nalini Anantharaman Annalisa Buffa Weinan E Irene Fonseca Isabelle Gallagher Martin Hairer Mike Hopkins Meena Mahajan Akshay Venkatesh Anna Wienhard Geordie Williamson The ICM Structure Committee is encouraged to interact with the mathematical community worldwide.
P3 This point is a key point of contention with Scholze?Stix, who claim that their omission of such labels do not affect the result. At this point in time, I cannot tell whether Scholze?Stix’s simplifications preserve structural information (their claim) or lose structural information (Mochizuki’s claim). These notes are to rather going to examine Mochizuki’s examples in the Report to find precise mathematical statements underlying them, and what thinking about them structurally can say. At times Mochizuki’s examples are formulated so that the structural content is unclear (mostly because the required categories are not supplied), and at times they are expressed in a material way, but with an underlying structural idea obscured by the jargon. I will start by considering an abstract category-theoretic setup that underlies several of Mochizuki’s examples, shorn of all irrelevant information and commentary.
P5 Mochizuki discusses ‘labels’ a lot, but it appears what is really meant is that for the purposes of considering (formal) colimits, one needs to not discard the domain of the diagram. It may well be that Mochizuki’s intention is to capture this idea, but his mode of expressing such a simple category-theoretic construction obscures its simplicity. One can look at (H1) and (H2) in the Report for instance, and wonder what ‘histories of operations’ is supposed to mean, or ‘re-initialization operations’. If the diagrams shown there are supposed to represent diagram shapes over which one is taking colimits, then it is a category-theoretic triviality that one gets different colimits (recall the quote of Freyd above!). (引用終り) 以上
Members & Partners The LPP-RIMS AHGT International Research Network is a France-Japan network between Laboratoire Paul Painleve of Lille University -- Algebraic and arithmetic geometry & Geometry and Topology, the DMA of ENS Paris PSL, and RIMS of Kyoto University as leading institutions, which regroups 45 researchers and a dozen PhD students in 16 universities as core members.
Germany ・Jakob Stix, Goethe-University Frankfurt USA ・Florian Pop, Univ. Pennsylvania ・Jordan Ellenberg, Univ. Wisconsin UK ・Ivan Fesenko, University of Warwick RIMS, Kyoto University ・Koshikawa Teruhisa ・Mochizuki Shinichi
https://ahgt.math.cnrs.fr/activities/ Activities & Workshops Mar 6, 2023 Genus zero modular operad and absolute Galois group by Noemie Combe, Max-Planck-Institut Leipzig, Germany. Apr 17, 2023 Anabelian geometry and m-step reconstruction by Yamaguchi Naganori, Tokyo Institute of Technology, Japan. May 15, 2023 Title [To be announced] by Adrien Dubouloz, Universite de Bourgogne - CNRS, France.
AHGT Workshops and Conferences Arithmetic Seminar Day in Toyonaka 2023 Osaka - Toyonaka Mar. 13, 2023 Org.: H. Nakamura Webpage of the workshop Arithmetic & Homotopic Galois Theory 2023 ENS-RIMS Zoom Hybrid Mar. 20-24, 2023 Org.: B. Collas, P. Debes, Y. Hoshi, A. Mezard Webpage of the workshop
>>261 math_jinいいね https://ツイッター/ math_jin 2月18日 We then proceed to survey recent developments (work in progress) in IUT,namely,the Galois-orbit version of IUT,which has new applications to the Section Conjecture(in anabelian geometry)and the nonexistence of Siegel zeroes of certain Dirichlet L-functions https://kurims.kyoto-u.ac.jp/~motizuki/Title%20and%20abstract%20(Shinichi%20Mochizuki,%20Workshop%20on%20Arithmetic%20and%20Homotopic%20Galois%20Theory%202023).pdf
論文を自分で読んで判断出来ないなら沈黙すべきなのに、擁護派も否定派も、誰々が批判しただの誰々が意見を変えただのと他人の尻馬に乗ってでレスバトルするだけ ずっとそうやって井戸端会議してればいいんじゃない？ working mathematicianなら、自分がフォローしてない議論について是非を語るなんて恥ずかしくて出来ないと思うけど笑
https://www.kurims.kyoto-u.ac.jp/~motizuki/IUT%20as%20an%20Anabelian%20Gateway.pdf INTER-UNIVERSAL TEICHMULLER THEORY AS ¨ AN ANABELIAN GATEWAY TO DIOPHANTINE GEOMETRY AND ANALYTIC NUMBER THEORY Shinichi Mochizuki (RIMS, Kyoto University) March 2023
§4. Brief preview of the Galois-orbit version of IUT (cf. “Expanding Horizons” videos/slides cited in §1) ・ New applications (work in progress!) of Galois-orbit version of IUT (GalOrbIUT):
なお、文中にあるが、下記は参考になるだろう [FskDsm]: //ivanfesenko.org/wp-content/uploads/2021/10/rapg.pdf ABOUT CERTAIN ASPECTS OF THE STUDY AND DISSEMINATION OF SHINICHI MOCHIZUKI’S IUT THEORY IVAN FESENKO （推測だが、これは2021年の版でしょう。下記のように、同じ題の2018版があったらしい）
>>369 ＞ネトウヨ期待のあの一件については賞も何もなし 確かにポジティブな方には何もなしでしたが、 ネガティブな方では証明が受け入れられていないということが再確認されました arXiv:2112.11598 >This proof has now been published in a serious research >journal, however it is clear that it is not accepted by the >mathematical community in general.
(参考) https://www.kurims.kyoto-u.ac.jp/~bcollas/Promenade-IUT/IUT-participants.html Promenade in IUT 2020.9～2021.4 List of Participants Pierre Debes, Lille University, FR; Seidai Yasuda, Osaka University, JP;
https://www.kurims.kyoto-u.ac.jp/~motizuki/RIMS-workshop-homepages-2016-2021/w4/iut2.html Inter-universal Teichmuller Theory (IUT) Summit 2021 RIMS workshop, September 7 - September 10 2021 Confirmed participants include: Pierre Debes (Univ. Lille, France),
https://ahgt.math.cnrs.fr/activities/workshops/AHGT-2023/ Arithmetic & Homotopic Galois Theory IRN 2023 List of participants Pierre Debes Universite de Lille Nakamura Hiroaki, Osaka University, Japan Hidekazu Furusho Nagoya university Yasuda Seidai, Hokkaido University, Japan Tadashi Ochiai Tokyo Institute of Technology Jakob Stix Goethe-University Frankfurt Florian Pop University of Pennsylvania
https://ahgt.math.cnrs.fr/activities/workshops/AHGT-2023/ Workshop - Arithmetic & Homotopic Galois Theory 2023 March 20 to 24, 2023 ・ ENS Paris & RIMS Kyoto [Hybrid] ・ Org.: B. Collas (RIMS), P. Debes (Lille), Y. Hoshi (RIMS), A. Mezard (ENS)
スレ主です １）F氏は 関ケ原の戦いは、もう勝った気でいると思うよｗ ２）>>590より https://ahgt.math.cnrs.fr/activities/workshops/AHGT-2023/ Workshop - Arithmetic & Homotopic Galois Theory 2023 March 20 to 24, 2023 ・ ENS Paris & RIMS Kyoto [Hybrid] ・ Org.: B. Collas (RIMS), P. Debes (Lille), Y. Hoshi (RIMS), A. Mezard (ENS) ここから、On-line attendance [46] Ivan Fesenko YMSC Tsinghua University and Univ Warwick 名前のIvan Fesenkoにリンクがあって、彼のページに飛べる //ivanfesenko.org/ だ News にアップされている下記、ここらを焼き直しして、プレゼンやりそうに思う //ivanfesenko.org/wp-content/uploads/Q/C1/partI.pdf Core topics in number theory I (algebraic number theory, class field theory) //ivanfesenko.org/wp-content/uploads/hatprob.pdf Problems in higher adelic theory, talk April 2023 Beijing //ivanfesenko.org/wp-content/uploads//Q/C1/q6m.pdf Anabelian geometry-IUT-effective abc inequalities-applications, YMSC/BIMSA number theory seminar talk, March 2023 ３）あと、IUT5人論文で若手のPorowski Wojciechというのがいて、いまRIMS 特定助教だ（下記） F氏のところでIUTネタでDRを取った F氏はボスとして、Porowski氏が食える（数学者としていい職を得る）ようにしてやる責務がある それには、IUTをぶち上げるのが、一番の早道だし、自分のPRにもなる （IUT5人論文の南出氏や星氏にも、IUT売り込みのおこぼれが行くだろう） https://www.kurims.kyoto-u.ac.jp/ja/list/porowski.html 京都大学数理解析研究所｜RIMS Porowski Wojciech 特定助教
１）望月IUTに対する数学的反論は、例のSS文書のみだが https://www.math.uni-bonn.de/people/scholze/WhyABCisStillaConjecture.pdf Scholze氏は このｐ4で 2.1.Glossary:IUTT-terminology and how we may think of these objects.の節で ”This will involve certain radical simplifications,and it might be argued that such simplifications strip away all the interesting mathematics that forms the core of Mochizuki's proof.” と書いているけど、これ将棋で言えば禁じ手で ”二歩”みたいなもの
うん、下記だね Ｆ氏の下記”[R12] Problems in higher adelic theory, talk April 2023 Beijing” （ここでは、IUTは HAT--2dLanglandsprogram? に位置づけられているね） これが、ICBSの”Higher adelic approach to the Tate-BSD conjecture”の講演に近そうだな
(参考) //www.icbs.cn/en/web/index/18009_1553670__ ICBS Satellite Conference on Algebraic and Arithmetic Geometry 14:30-15:30 Ivan Fesenko (Warwick University and Tsinghua University) Higher adelic approach to the Tate-BSD conjecture I will first present basics of two adelic structures on relative elliptic surfaces over Spec of the ring of integers of a number field or a smooth projective irreducible curve over a finite field and of the higher adelic zeta integral. Then I will concentrate on the higher adelic program to prove the equality of the arithmetic and analytic ranks of the generic fibre.
//ivanfesenko.org/?page_id=126 Research ? Ivan Fesenko //ivanfesenko.org/wp-content/uploads/hatprob.pdf [R12] Problems in higher adelic theory, talk April 2023 Beijing P9/24 ここの図の右下に HAT--IUT とある（IUT成立は認め過去完了扱い） （なお、この図はＦ氏のIUT関連文書で頻繁に出てくる図）
（関連） //ivanfesenko.org/?page_id=126 K 2d adelic analysis and geometry, and applications W. Czerniawska, Higher adelic programme, adelic Riemann-Roch theorems and the BSD conjecture, PhD thesis, eprints Nottingham 2018
コピーペースト下記 Here are some relations between the three generalisations of CFT and their further developments:
2dLC?－－ 2dAAG－－－ IUT l ／ ｜ ｜ l ／ ｜ ｜ l／ ｜ ｜ LC 2dCFT anabelian geometry ＼ ｜ ／ ＼ ｜ ／ ＼ ｜ ／ CFT 注）記号： Class Field Theory (CFT), Langlands correspondences (LC), 2dAAG = 2d adelic analysis and geometry, two-dimensional (2d) (P8 "These generalisations use fundamental groups: the etale fundamental group in anabelian geometry, representations of the etale fundamental group (thus, forgetting something very essential about the full fundamental group) in Langlands correspondences and the (abelian) motivic A1 fundamental group (i.e. Milnor K2) in two-dimensional (2d) higher class field theory.") https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/documents/Fesenko%20-%20IUT%20and%20modern%20number%20theory.pdf Fesenko IUT and modern number theory
https://www.icbs.cn/en/web/index/18009_1553670__ Schedule July 12th 14:30-15:30 Ivan Fesenko (Warwick University and Tsinghua University) Higher adelic approach to the Tate-BSD conjecture I will first present basics of two adelic structures on relative elliptic surfaces over Spec of the ring of integers of a number field or a smooth projective irreducible curve over a finite field and of the higher adelic zeta integral. Then I will concentrate on the higher adelic program to prove the equality of the arithmetic and analytic ranks of the generic fibre.
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ ホッブズは人間の自然状態を、 決定的な能力差の無い個人同士が互いに自然権を行使し合った結果としての 万人の万人に対する闘争（羅: bellum omnium contra omnes, 英: the war of all against all）であるとし、 この混乱状況を避け、共生・平和・正義のための自然法を達成するためには、 「人間が天賦の権利として持ちうる自然権を国家（コモンウェルス）に対して 全部譲渡（と言う社会契約を）するべきである。」 と述べ、社会契約説を用いて、従来の王権神授説に代わる絶対王政を合理化する理論を構築した。 ホッブズはこの国家（コモンウェルス）を指して「リヴァイアサン」と言っている[2]。
大学教授 Alexander Pruss氏>>880 が否定派ですね 彼は、数学DRからphilosophyに転向した人のようです
https://en.wikipedia.org/wiki/Alexander_Pruss Alexander Robert Pruss (born January 5, 1973) Biography After earning a Ph.D. in mathematics at the University of British Columbia with a dissertation on Symmetrization, Green’s Functions, Harmonic Measures and Difference Equations, under John J. F. Fournier in 1996, and publishing several papers in Proceedings of the American Mathematical Society and other mathematical journals,
>彼は、下記 mathoverflowで質問者に、否定的な回答をしています >” we have no reason to think that the conglomerability assumption is appropriate.”だと conglomerability assumption はPrussの勘違いであり、箱入り無数目とは関係ありません。 その証拠に後にPrussは箱入り無数目は成立だと撤回しています。 For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here isn't in the probabilistic sense), we win with probability at least (n-1)/n. That's right.
>大学教授 Alexander Pruss氏>>880 >が否定派ですね 嘘はダメですよ？ Prussは箱入り無数目成立を明言しています。 For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here isn't in the probabilistic sense), we win with probability at least (n-1)/n. That's right.
>>884 >Prussは箱入り無数目成立を明言しています。 >For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here >isn't in the probabilistic sense), we win with probability at least (n-1)/n. That's right.
ここは、高校生も来るかも知れないので、指摘しておきますが 典型的な詭弁ですね
つまり、全文引用すると https://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice 2 What we have then is this: For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here isn't in the probabilistic sense), we win with probability at least (n?1)/n. That's right. But now the question is whether we can translate this to a statement without the conditional "For each fixed opponent strategy". - Alexander Pruss Dec 19, 2013 at 15:05 (引用終り)
追伸 ついでに、Alexander Prussの前日の発言を下記に引用します 両方合わせないと、彼の主張が分からないでしょうから I was assuming that "independently" has the meaning it does in probability theory (P(AB)=P(A)P(B) and generalizations for σ-fields). But that does require a probabilistic description of the opponent's choice. Of course, one could mean "independently" here in some non-mathematical causal sense. (And there may be philosophical reason for doing this: fitelson.org/doi.pdf http://fitelson.org/doi.pdf ) Still, mixing the probabilistic with nonprobabilistic concepts might lead to some difficulties, though. ? Alexander Pruss Dec 18, 2013 at 15:21
That "for [each] fixed sequence, the probability of failing is at most 1/N" basically says something like that P(F|S)=1/N for each sequence S. But you can't infer that P(F)=1/N unless you've got a probability measure on the whole space conglomerable with respect to the partition induced by the Ss. (I bet the probabilities are going to be at best finitely additive, and if we have merely finitely additive probabilities, we can have failures of conglomerability.) I am reminded of the Brown-Freiling argument against CH.
1）ここで、i は前段から ”Let's go back to the riddle. Suppose u^→ is chosen randomly. The most natural option is that it is a nontrivial i.i.d. sequence (uk), independent of the random index i which is uniformly distributed over [100]={0,...,99}. In general, Mj will be nonmeasurable (one can prove this in at least some cases). We likewise have no reason to think that M is measurable. But without measurability, we can't make sense of talk of the probability that the guess will be correct.” と書かれていて、”independent of the random index i which is uniformly distributed over [100]={0,...,99}” ですね。 まず、”if i is chosen uniformly independently of that strategy”の成立に疑問が呈されています そして、カッコ内の”(where the "independently" here isn't in the probabilistic sense)”にも、疑問符つきですね 2）よって、上記1）の二つの疑問点を、Pruss氏は呈しています 3）Pruss氏は、全体として、箱入り無数目類似の”Probabilities in a riddle involving axiom of choice” を、否定しています
>>902 >まず、”if i is chosen uniformly independently of that strategy”の成立に疑問が呈されています 呈してないｗ iを{0,1,...,99}上の一様分布で選択したら、当然出題列とは独立だバカｗ
>そして、カッコ内の”(where the "independently" here isn't in the probabilistic sense)”にも、疑問符つきですね どこに疑問符がついてるの？バカ？ where は関係副詞であって疑問詞じゃないよ 中学英語ｗ しかもここの意味は「この『独立』というのは『確率論における独立』の意味ではない」という誰でも分かる当たり前のことしか言ってない 初歩の初歩から分かってなくて草
>2）よって、上記1）の二つの疑問点を、Pruss氏は呈しています 呈していないｗ
>3）Pruss氏は、全体として、箱入り無数目類似の”Probabilities in a riddle involving axiom of choice” > を、否定しています 否定していないｗ
we win with probability at least (n-1)/n. That's right. はどこ行っちゃったんだよｗ 「我々（回答者）が確率(n-1)/n以上で勝つ、それは正しい。」 って明言してるじゃねーかｗ
全文引用 What we have then is this: For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here isn't in the probabilistic sense), we win with probability at least (n－1)/n. That's right. But now the question is whether we can translate this to a statement without the conditional "For each fixed opponent strategy". – Alexander Pruss Dec 19, 2013 at 15:05
