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 0230１３２人目の素数さん2023/01/29(日) 20:54:50.46ID:qSKMe8KO このスレで査読をする能力のありそうなやつ見たことないから、 群盲象をなんとか状態じゃん 0231１３２人目の素数さん2023/01/29(日) 20:56:10.21ID:qSKMe8KO>>225 悪いとかなんとかではなく、きちんと論理的にいわんと。 0232１３２人目の素数さん2023/01/30(月) 13:00:29.73ID:wStpJW+D>>230 元のIUTが説明出来てないんだがw 0233１３２人目の素数さん2023/01/30(月) 13:15:48.87ID:jB5TaMHo ヲワタ 0234１３２人目の素数さん2023/01/30(月) 14:27:42.70ID:eaEabJ4k rimsとkodaiでは成功してる 0235１３２人目の素数さん2023/01/30(月) 16:02:44.08ID:EVwMk0cs まぁ応援スレでは夢見とけばいいかもな 0236１３２人目の素数さん2023/02/01(水) 16:11:30.39ID:sQMfVFbD メモ https://taro-nishino.blogspot.com/2019/03/blog-post064.html TARO-NISHINOの日記 数学における最大の謎: 望月新一と不可解な証明 3月 24, 2019 今回紹介するのは2015年10月のNature誌に載っていた"The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof"です。 https://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509
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 0256１３２人目の素数さん2023/02/19(日) 20:10:36.69ID:ynjTT/Eh>>255 >Ivan Fesenko, University of Warwick？ 大学変わった？
これか https://webcache.googleusercontent.com/search?q=cache:nfSLRDd7tjwJ:https://twitter.com/math_jin/status/1468329113672818692&cd=1&hl=ja&ct=clnk&gl=jp math_jin Fesenko氏の所属が変わっていた。 (Ivan Fesenko) Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom Translate Tweet 9:18 PM ・ Dec 7, 2021
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): 0277１３２人目の素数さん2023/02/24(金) 17:13:36.53ID:X3N7nH4d 次はリーマン予想の証明だろう。 0278１３２人目の素数さん2023/03/05(日) 08:27:41.56ID:5TZmfx+E なるほど
じゃあ、Siegel zero が存在しないことを証明してもリーマン予想の証明にはならない、ということか。 0312１３２人目の素数さん2023/04/19(水) 21:28:24.44ID:eQ93QFKa Siegel zero が存在しないことを証明してもリーマン予想の証明にはならない が もし、Siegel zero が存在しないことを証明できたら ビッグニュースになるだろうね
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）
https://www.reddit.com/r/math/comments/9lxyry/ivan_fesenko_on_current_iutt_situation_about/ Posted by u/Wojowu Number Theory5 years ago（Oct 07,2018） Ivan Fesenko on current IUTT situation: "About certain aspects of the study and dissemination of Shinichi Mochizuki's IUT theory" maths.nottingham.ac.uk/plp/pm... (引用終り) 以上 0316１３２人目の素数さん2023/04/25(火) 10:20:49.21ID:SWELEy0k ABC予想は確かに証明されている
これが事実だ。 京大数理解析研ではabc予想の証明を 書いた望月論文が受理される前から、 abc予想が解決したと公文書で公表した。 0317１３２人目の素数さん2023/04/25(火) 18:56:36.97ID:aFvtap8I Mochizuki’s Corollary 3.12 and my quest for its proof
