（前“応援”スレが、1000又は1000近くになったので、新スレ立てる） 前スレ：Inter-universal geometry と ABC予想 (応援スレ) 70 https://rio2016.5ch.net/test/read.cgi/math/1701399491/ 詳しいテンプレは、下記旧スレへのリンク先ご参照 Inter-universal geometry と ABC予想 (応援スレ) 52 https://rio2016.5ch.net/test/read.cgi/math/1613784152/1-13 ＜IUT最新文書＞ https://www.kurims.kyoto-u.ac.jp/~motizuki/news-japanese.html 2024年03月24日 望月新一 ・（過去と現在の研究）2024年4月に開催予定のIUGCの研究集会での講演の スライドを公開。https://www.kurims.kyoto-u.ac.jp/~motizuki/IUT%20as%20an%20Anabelian%20Gateway%20(IUGC2024%20version).pdf P8 In this context, it is important to remember that, just like SGA, IUT is formulated entirely in the framework of “ZFCG” (i.e., ZFC + Grothendieck’s axiom on the existence of universes), especially when considering various set-theoretic/foundational subtleties (?) of “gluing” operations in IUT (cf. [EssLgc], §1.5,§3.8,§3.9, as well as [EssLgc],§3.10, especially the discussion of “log-shift adjustment” in (Stp 7)): (引用終り)
https://www3.nhk.or.jp/news/html/20230707/k10014121791000.html NHK 数学「ABC予想」新たな証明理論の研究発展させる論文に賞創設 20230707 数学の難問「ABC予想」を証明したとする日本の数学者の新たな理論をめぐって、研究を発展させる論文を対象に、100万ドルの賞金を贈呈する賞が国内のIT企業の創業者によって創設されることになりました。 ▽新たな発展を含む論文を毎年選び、最大で賞金10万ドル ▽理論の本質的な欠陥を示す論文を発表した最初の執筆者に対しては100万ドルを、 それぞれ贈呈するとしています。
https://ahgt.math.cnrs.fr/activities/ Anabelian Geometry and Representations of Fundamental Groups. Oberwolfach workshop MFO-RIMS Sep. 29-Oct. 4, 2024 Org.: A. Cadoret, F. Pop, J. Stix, A.. Topaz （J. Stixさん、IUT支持側へ）
https://pmb.centre-mersenne.org/articles/10.5802/pmb.58/ The abcd conjecture, uniform boundedness, and dynamical systems Robin Zhang1, 2 Publications mathématiques de Besançon. Algèbre et théorie des nombres (2024), pp. 119-134.
We survey Vojta’s higher-dim
665 名前：ensional generalizations of the abc conjecture and Szpiro’s conjecture as well as recent developments that apply them to various problems in arithmetic dynamics. In particular, the “abcd conjecture” implies a dynamical analogue of a conjecture on the uniform boundedness of torsion points and a dynamical analogue of Lang’s conjecture on lower bounds for canonical heights.
[49] Shinichi Mochizuki; Ivan Fesenko; Yuichiro Hoshi; Arata Minamide; Wojciech Porowski Explicit estimates in inter-universal Teichmüller theory, Kodai Math. J., Volume 45 (2022) no. 2, pp. 175-236 | Zbl []
さらに、ちょっと検索したら、一つヒットしただけで、他にあるかもしらんぜｗ さらに、”The abcd conjecture, uniform boundedness, and dynamical systems Robin Zhang1, 2 Publications mathématiques de Besançon. Algèbre et théorie des nombres (2024)” とあるよね
5人論文 [49] Shinichi Mochizuki; Ivan Fesenko; Yuichiro Hoshi; Arata Minamide; Wojciech Porowski Explicit estimates in inter-universal Teichmüller theory, Kodai Math. J., Volume 45 (2022) no. 2, pp. 175-236 だから、2022～2024 のたった２年間だ これからどうなるかは、請うご期待ですｗｗ
https://pmb.centre-mersenne.org/articles/10.5802/pmb.58/ The abcd conjecture, uniform boundedness, and dynamical systems Robin Zhang1, 2 Publications mathématiques de Besançon. Algèbre et théorie des nombres (2024), pp. 119-134.
We survey Vojta’s higher-dimensional generalizations of the abc conjecture and Szpiro’s conjecture as well as recent developments that apply them to various problems in arithmetic dynamics. In particular, the “abcd conjecture” implies a dynamical analogue of a conjecture on the uniform boundedness of torsion points and a dynamical analogue of Lang’s conjecture on lower bounds for canonical heights.
[49] Shinichi Mochizuki; Ivan Fesenko; Yuichiro Hoshi; Arata Minamide; Wojciech Porowski Explicit estimates in inter-universal Teichmüller theory, Kodai Math. J., Volume 45 (2022) no. 2, pp. 175-236 | Zbl
・例えば、下記は現在進行形の集会が下記 https://ahgt.math.cnrs.fr/ Arithmetic & Homotopic Galois Theory IRN The LPP-RIMS Arithmetic & Homotopic Galois Theory IRN (AHGT) is a CNRS France-Japan International Research Network between Lille University (Laboratoire de Mathématiques Paul Painlevé), École Normale Supérieure - PSL (Département de Mathématiques et Applications), and the Research Institute for Mathematical Sciences, Kyoto University. Coordinators: B. Collas° (RIMS, JP), Y. Hoshi (RIMS, JP), B. Fresse (Lille, FR), A. Mézard (ENS, FR). Sponsors: P. Dèbes (Lille, FR) & A. Tamagawa (RIMS, JP)
https://fr.wikipedia.org/wiki/Ariane_M%C3%A9zard Ariane Mézard Ariane Mézard est une mathématicienne française et professeure de mathématiques à Sorbonne-Université et à l'ENS qui travaille en géométrie arithmétique.
https://webusers.imj-prg.fr/~ariane.mezard/ Ariane Mézard Professeur Département de Mathématiques et Applications Ecole Normale Supérieure de Paris
https://rio2016.5ch.net/test/read.cgi/math/1719537780/406 より １）君は、ほんとうに数学に向いていないねｗ 思考が、”Elliptic geometry”（下記）だね。本来、直線として筋を通すべきところが グネグネ曲がる曲線思考になるんだ 本来、そういう結論にならないのに、カーブがかかっておかしな結論に至る (参考) https://en.wikipedia.org/wiki/Elliptic_geometry Elliptic geometry Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. (引用終り)
＜IUTカンファレンス３回の参加者リスト＞ https://zen.ac.jp/iugc/activities/events 第１回 IUGCカンファレンス オーガナイザー 星 裕一郎 加藤 文元 望月 新一 2024年4月2日〜 4月5日 東京 [List of speakers] Yuichiro Hoshi(RIMS) Emmanuel Lepage(IMJ-PRG) Arata Minamide(RIMS) Shinichi Mochizuki(RIMS) Wojciech Porowski(RIMS) Shota Tsujimura(RIMS) Go Yamashita(RIMS) [Current list of participants] James Douglas Boyd(Western Ontario) Benjamin Collas(RIMS) Weronika Czerniawska(Westlake) Pa
768 名前：olo Dolce(Westlake) Taylor Dupuy(Vermont) Ivan Fesenko(IUGC, Westlake) Fumiharu Kato(IUGC, Tokyo Tech) Kiran Kedlaya(UCSD) Jeff Lagarias(Michigan) Masatoshi Suzuki(Tokyo Tech.) Seidai Yasuda(Hokkaido) KAJI, Hajime(Waseda） Yukiyoshi Nakajima(Tokyo Denki） Atsushi Katsuda(Kyushu） Yuki Goto(Keio） Yu Yasufuku(Waseda） Kei Hagihara(Keio） Akishi Kato(Tokyo） ShunsukeTada(Kobe） Shoudai Furuhata(Waseda） Naganori Yamaguchi(Tokyo Tech） Toshiyuki Katsura(Tokyo） Maeda Naoya(JAIST） Shiyuan Wan(Bordeaux） Sang Geun Han(KAIST） Lucas Hiroyuki Ragni Hamada(Tokyo Tech） Katsunori Takahashi(CreateArk Inc.） Yuya Kanado(Nagoya） Erol Serbest(Yeditepe） Ali Bleybel(Lebanese） Hiro-aki Narita(Waseda） Qixiang Wang(Paris-Saclay） Junghwan Lim(Industry） Ruicong Rong(Heidelberg） Masaki Sakamoto(Tokyo Metropolitan） Akihiro Yamashita(Tokyo Metropolitan） Kanau Shimada(Tokyo） Yongpan Zou(Tokyo） Afonso de Assis( IST(Instituto Superior Técnico) Lisbon, Portugal） Katsumi Imaizumi(TOPPAN Digital Inc.） Reiya Tachihara(RIMS） Mateo Carmona(Istituto Grothendieck） Shun Yin(School of Mathematical Science, Peking） Takaaki Harada(Yokohama National） Shane KELLY(Tokyo） Sean B Lynch(UNSW Sydney） Yuki Kondo(Osaka） Xiao WangSun Yat-sen） Sun ZemingRIMS） Rein Janssen GroesbeekIMJ-PRG）
https://ahgt.math.cnrs.fr/activities/workshops/MFO-RIMS23/ MFO-RIMS Tandem workshop 2023 - Arithmetic Homotopy and Galois Theory List of invited participants Following the Oberwolfachinstitute tradition, attendance to this workshop is by invitation and, with a few exceptional grounds, in person only. Site RIMS Kyoto, Japan Anna Cadoret Sorbonne Université Benjamin Collas RIMS - Kyoto Vasily Dolguchev Temple David Harbater of Pennsylvania Tim Holzschuh Heidelberg Akinari Hoshi Niigata Yu Iijima Hiroshima Shun Ishii Keio Joachim König Korea National of Education Arata Minamide RIMS - Kyoto Shinichi Mochizuki RIMS - Kyoto Takahiro Murotani Tokyo Institute of Technology Ariane Mézard ENS PSL Tadashi Ochiai Tokyo Institute of Technology Séverin Philip RIMS - Kyoto Wojciech Porowski RIMS - Kyoto Koichiro Sawada RIMS - Kyoto Densuke Shiraishi Osaka Yuichiro Taguchi Tokyo Institute of Technology Akio Tamagawa RIMS - Kyoto Shota Tsujimura RIMS - Kyoto Naganori Yamaguchi Tokyo Institute of Technology Go Yamashita RIMS - Kyoto Yu Yang RIMS - Kyoto Seidai Yasuda Hokkaido
Site Oberwolfach, Germany Antonin Assoun Université de Lille Lior Bary-soroker Tel Aviv Angelot Behajaina Technion Israel Institute of Tech. Alexander Betts Harvard Frauke Bleher of Iowa Elyes Boughattas Université Sorbonne Paris Nord Ted Chinb
770 名前：urg Pennsylvania Noemie Combe MPI for Mathematics in Sciences David Corwin Ben Gurion of the Negev Cyril Demarche Sorbonne Université Philip Dittmann Technische Universität Dresden Pierre Dèbes Lille Arno Fehm Technische Universität Dresden David Harari Paris Saclay Yuichiro Hoshi RIMS - Kyoto Valentijn Karemaker Utrecht François Legrand Guangdong Technion Israel IT Emmanuel Lepage Sorbonne Université Daniel Litt of Toronto Martin Lüdtke Rijksuniversiteit Groningen Hiroaki Nakamura Osaka Danny Neftin Technion Israel Institute of Tech. Stephan Patrikis Ohio State Florian Pop Pennsylvania Rachel Pries Colorado State Gereon Quick Trondheim Christopher Rasmussen Wesleyan Tomer Schlank Einstein Institute of Mathematics Béranger Seguin Université de Lille Roy Shmueli Tel Aviv Naotake Takao RIMS - Kyoto Adam Topaz of Alberta Craig Westerland of Minnesota
(参考) https://ahgt.math.cnrs.fr/activities/#the-ahgt-seminar Arithmetic & Homotopic Galois Theory IRN Activities - Conferences & Seminars Next coming talks… ・May 13, 2024 Double shuffle torsor of cyclotomic multiple zeta values and stabilizers of de Rham and Betti coproducts by Khalef Yaddaden, Nagoya University, Japan. ・Jun 3, 2024 Towards Uniform Finiteness Results on Heavenly Elliptic Curves by Christopher Rasmussen, Wesleyan University, USA. ・Jul 1, 2024 On the reducibility of fibers of polynomials by Angelot Behajaina, Technion & Open University of Israel.
Anabelian Geometry and Representations of Fundamental Groups. Oberwolfach workshop MFO-RIMS ・Sep. 29-Oct. 4, 2024 Org.: A. Cadoret, F. Pop, J. Stix, A.. Topaz
Arithmetic Homotopy & Galois Theory. Oberwolfach-RIMS tandem workshop MFO-RIMS ・Sep. 24-29, 2023 Org.: B. Collas, P. Dèbes, Y. Hoshi, A. Mézard
Paris Arithmetic Homotopy Galois Theory Day 2024 Paris IMJ-PRG (Jussieu), France ・Sept. 23-24, 2024 Org.: B. Collas, E. Lepage
Lecture on ``Berkovich methods for anabelian reconstructions and Resolution of Nonsingularities'' RIMS, Japan ・April 8, 10 and 12, 2024 By E. Lepage (IMJ Paris, France)
Anabelian Geometry in Tokyo 2024 Tokyo, Japan ・Mar. 11-22, 2024 Org.: Y. Taguchi, T. Murotani, N. Yamaguchi (Tokyo Inst. Tech.)
Workshop on Model theory of valued fields and applications. Lille ・Feb. 19-21, 2024 Org.: R. Cluckers (CNRS-Lille), A. Forey (CNRS-Lille), Y. Hendel (KU Leuven)
Spaces and perfectoids Paris & RIMS Kyoto [Bridge] ・July 19, 2024 Org.: M. Ferreira-Filoramo, S. Philip & N. Takada & N. Yamaguchi
Around the Grothendieck-Teichmüller group Paris & RIMS Kyoto [Bridge] ・Feb. 27, 2024 Org.: M. Ferreira-Filoramo, S. Philip & N. Yamaguchi
(参考) https://www.math.uni-bonn.de/people/scholze/WhyABCisStillaConjecture.pdf Why abc is still a conjecture PETER SCHOLZE AND JAKOB STIX Date: July 16, 2018. 2.1. Glossary: IUTT-terminology and how we may think of these objects. The IUTT papers introduce a large amount of terminology. To facilitate the discussion, we will describe (only) the notions that are strictly relevant to explain what we regard as the error. 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. <google訳の手直し> IUTT の論文では、大量の用語が使用されています。 議論を容易にするために、 ここでは、エラーと見なすものを説明するために厳密に関連する概念 (のみ) について説明します。 これには、いくつかの根本的な単純化が伴いますが、 これにはある根本的な単純化が伴い、そのような単純化は望月の証明の核となる興味深い数学をすべて取り除いてしまうという議論もあるかもしれない。 この反論に対しては4つの言い訳ができる。
(参考) https://eow.alc.co.jp/search?q=%E3%82%8F%E3%82%89%E4%BA%BA%E5%BD%A2%E8%AB%96%E6%B3%95 英辞郎 on the WEB わら人形論法 straw-man argument〈批判的〉〔反論に都合がいいように論争相手の主張をねじ曲げ（または相手の主張と関係ない論点を持ち出し）、そのすり替えられた論点に対して反論を行うこと（そして「だから相手の主張は間違っている」と結論すること）。〕
795 名前：１３２人目の素数さん [2024/07/10(水) 09:36
]
[ここ壊れてます]
796 名前：:11.69 ID:eCNf9s7z.net mailto: >>731 専門分野が違えばショルツでもいっちょ噛みになる世界なんだよ RIMSは外部から差読者入れてて、望月教授の再反論に沈黙してるのはショルツだぞ しかもショルツの反論の方が査読なしの特別寄稿で abc is still conjectureとか消極的タイトルで、IUT is wrongとは言ってないクソ文章なんよ はっきり言って健全な議論の振りして研究所に泥塗って 望月教授が沈黙しているかのようなツラして 白々しく健康を気づかってるショルツのがこの件にかんしてはゴミ野郎なんだよ []
あれは、望月氏の暴言が問題で、ショルツ氏をオチコボレ院生呼ばわりしたことが原因 （下記 This Remark may be described as a breath-takingly (melo?)dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level. ） Stix氏も切れてしまったみたい そう思っています だから、SS側は 「Mochizuki氏とは冷静な議論が出来ないな」と判断したのでしょうか
(参考) https://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html 2018年3月、数理研で行なわれたIUTeichに関する議論を纏めた報告書 （および関連文書） https://www.kurims.kyoto-u.ac.jp/~motizuki/Cmt2018-08.pdf Shinichi Mochizuki July 2018 COMMENTS ON THE MANUSCRIPT (2018-08 VERSION) BY SCHOLZE-STIX CONCERNING INTER-UNIVERSAL TEICHM¨ ULLER THEORY (IUTCH) Shinichi Mochizuki September 2018 Ｐ１ (C1) : Remark 5, “For fixed ... h(P) ≤ b.”: I can only say that it is a very challenging task to document the depth of my astonishment when I first read this Remark! This Remark may be described as a breath-takingly (melo?)dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level.
To repeat, this sort of argument lies well within the framework of advanced undergraduate/beginning graduate-level mathematics. It is entirely inconceivable that any researcher with substantial experience working with heights of rational points would attempt to prove this sort of finiteness statement by invoking such a nontrivial result as Faltings’ theorem.
(参考) https://en.wikipedia...ki/Elliptic_geometry Elliptic geometry Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect.
(参考) https://www.kurims.kyoto-u.ac.jp/~motizuki/travel-japanese.html 望月 出張講演 https://www.kurims.kyoto-u.ac.jp/~motizuki/IUT%20as%20an%20Anabelian%20Gateway%20(MFO-RIMS23%20version).pdf [21] Inter-universal Teichmuller Theory as an Anabelian Gateway to Diophantine Geometry and Analytic Number Theory (MFO-RIMS Tandem Workshop "Arithmetic Homotopic & Galois Theory" (Zoom) 2023年09月27日） Lecture Notes
”jinさん”がヒントで jinさんのX（旧ツイッター）から、下記に辿り着く (参考) https://ahgt.math.cnrs.fr/videos/page3/index.html AHGT Video Series IUT as anabelian gateway to diophantine geometry and analytic number theory (S.Mochizuki) On Mar 22, 2023 From Kyoto Japan Event ``Arithmetic & Homotopic Galois Theory 2023''
ところで、 >>771より再録。ユーツベになると、”文字起こし”機能が使える。>>775の質問と回答部分(らしき箇所)を抜粋しておきました （URLが通らないので略す） Mochizuki - IUT as anabelian gateway to diophantine geometry and analytic number theory Arithmetic & Homotopic Galois Theory - Mathematics 2023/09/19 文字起こし ＜質問部分＞ 49:47 [Music] for uh um along the cell multiplication one video is a multiple uh is this gluing supposed to lead to a structure that is so output structure will be described [Music] that was my question yes
50:24 I think that I understood with the lectures that you are kind of constructing some analog of the P1 of R actually so you are gluing R uh with itself uh using this green and so I think you are producing a set is it correct uh I see so so you're asking about what the structure is that so so what the structure that corresponds to p100 so there's the entirety uh once you lose this what is the object that corresponds to P1 is that for the first one the question was what's the point because I I was reading the slides and so uh I saw that you were doing this gluing of r with itself along the map I don't which was kind of identification of uh uh so the um elements of one side with the some non-zeroidance or the other side doing the the power map and so my uh so my reaction was what does we what do we obtain obtain after such a gluing and so my impression is that what you are obtaining is kind of a set is it correct so you just get the same one that plays in particular are said um so a top watch diagram uh consisting of um um so in particular one of Payne's various steps that associated with this diagram
um uh but the the point so this is another point that I I actually was endemic today so it's important always to specify the type of object that one is dealing with because um typically when only works with um not with a specific set theoretic object but an objects so important so this is briefly mentioned in section two it's it's sort of analogous that the SGA one situation or more traffic is equal to the notion of the objective closure there's the algebraic pleasure is never a specific said it's it's it's always defined after isomorphism there's no Natural Choice associated with so when when specifies the the type of object which is the algebraic culture so it's an important always to specify the type of object and typically um when only nodes what what only obtains so these instructions are give rise to uh various objects that are of a certain type and they're only defined up to it to really like someone's um so so there are various sets that you can associate with in these objects but sort of the main the main the main way that one one works is with with diagrams of various types of objects that are multiplying that and so this is also important because when when throughout all the because throughout the whole discussion so this also appears in section two when it wants to apply various out an obelian reconstruction algorithms and so already end up being reconstruction algorithms appeared in various talks previously one fundamental aspect of the Indian reconstruction algorithms is that even though when you use the word reconstruction one doesn't actually so another big one starts for instance what occurred and then when the president end up getting the construction algorithm to reconstruct the curve from a strictly set periodic point of view will never reconstructs precisely the same thing when it reconstructs occur and and there's a there's a natural there's a mortgage in them typically that isolation is very limited in fact there's some sort of the return of the scene but it's as I've said it's never precisely the same set so what only reconstructs things up to to ice similar to it
＜回答部分＞ 55:28 uh [Music] so yeah I'm not sure if this this thank you so I I was trying to to read the the slides a very uh uh simple mindedly so so that's why so it's also have the first question so but uh then uh I did not follow the restroom thank you so of course I guess another point so that I intended to make actually was that um another topic that has appeared in various thoughts and I think will appear
874 名前： in other times is is GP for the first time users um uh certain results concerning DP uh in them and so I think previously um GT was was not related to this sort of um uh this sorts of uh number three aspects uh but uh this also gives a new relationship foreign [Music] [Music]
so so you want me to say a few things about the indeterminacies so so um right so the the various kinds of in determinacies that but in fact the most um important in determinacy is what is called the M3 indeterminacy which arises from the logarithm is that uh so um if you think of the situation where R is the uh the Ring of integers um uh a local field work um uh in that sort of situation so here we're reconstructing so the common data that we have that's the input data for the Reconstruction is basically because of monoids and oh I'm sorry um and Abstract groups so but we would also like to reconstruct the additive spectrum and so at the local level the logarithm allows one to pass from The Notebook of monoid of units to the uh the average structure of the local field and so on the other hand [Music] um what was the sort of act as if um one doesn't need to do this so in other words will wants to consider invariance with respect is let's say one wants to consider objects that um where you can't tell the difference between not being anything and that gives rise to uh if you think about the way the Piano Works um on our units so in in you how's this a very non-trivial transformation but but um there's an the important observation is that there's an upper bound if you apply the logarithm and then take the units again it's a you can never leave the hell upon it's very complicated to if you try to trace the hidden element is that there are always some uh and combat set which is the large cells and [Music] um uh so this is looking at this up or down to my inequality so it's not [Music] um [Music] and uh uh so although there are many uh there are many independencies that occur in the UT sort of from the point of view of even numerically from the point of view uh uh uh balance of the heights uh on the height uh the main contribution is from this industry religions together a normal normal questions comments so uh I guess [Music] 1:02:47 let's thank the speaker again thanks thank you very much (引用終り) 以上
1）宇宙 (数学) ja.wikipedia.org/wiki/%E5%AE%87%E5%AE%99_(%E6%95%B0%E5%AD%A6) 集合論や数学基礎論における宇宙とは、特定の状況において考察される実体のすべてを元として含むような類のことである 圏論 圏論に歴史的につながる宇宙への別のアプローチの方法がある。これはグロタンディーク宇宙と呼ばれる。大まかに言えば、グロタンディーク宇宙とは集合論の通常実行されるすべての操作を内部にもつ集合である。例えば、グロタンディーク宇宙 U における2つの集合の和集合も U の内部にある。同様に、共通部分、順序対、冪集合などもまた U の内部にある。これは上記の上部構造に類似している。グロタンディーク宇宙の利点は、それが実際の集合であって真のクラスではないことである
V は二つの理由によって、“全ての集合による集合” とは異なるものである。第一に、これは集合ではない。各階層Vα がそれぞれ集合でも、その和である V は真のクラスであるからだ。第二に、V の要素は全て整礎集合に限られている。正則性公理は全ての集合が整礎的であることを要求していて、だからZFCでは全ての集合が V に属する。しかし、正則性公理を除いたり否定するような別の公理系を考えることも可能である（例えばアクゼルの反基礎公理（英語版））。 []
ところが、 『Grothendieck宇宙は 集合ですか クラスですか？（YES/NO）』 で、こちらは 『Grothendieck宇宙は a:集合ですか b:クラスですか？（a or b）』 としないと、前段の文と後段と平仄があっていない。つまり、（YES/NO）→（a or b）に変更要ですｗ
さて、フォン・ノイマン宇宙 V は、”遺伝的（英語版）整礎集合全体のクラス”>>829とある通りです つまり、クラスに属するものです。が、基礎論で特殊な役割をするクラスです
次に、Grothendieck宇宙も b:クラスですね Grothendieck宇宙は、フォン・ノイマン宇宙 V よりも真に大きく フォン・ノイマン宇宙 V を包含しますから 集合では収まらない （下記 グロタンディーク宇宙と到達不能基数 ご参照） よって、クラスに属するものです。基礎論で特殊な役割をするクラスであることは、フォン・ノイマン宇宙 V と同じです
>>839 >>Grothendieck宇宙はGrothendieck宇宙の公理が存在を保証する集合です >https://ja.wikipedia.org/wiki/%E3%82%B0%E3%83%AD%E3%82%BF%E3%83%B3%E3%83%87%E3%82%A3%E3%83%BC%E3%82%AF%E5%AE%87%E5%AE%99 >の冒頭に書いてあります >＞フォン・ノイマン宇宙 V よりも真に大きく >なんて少しでも内実を理解していれば出ない言葉です
あなたも賢くないのでは？ ja.wikipediaだけを見てもねぇｗ
1）下記 en.wikipedia Grothendieck universe より ”However, strongly inaccessible cardinals are on the lower end of the list of large cardinals; thus, most set theories that use large cardinals (such as "ZFC plus there is a measurable cardinal", "ZFC plus there are infinitely many Woodin cardinals") will prove that Grothendieck universes exist.” とありますぜｗ 2）もし、Grothendieck宇宙が フォン・ノイマン宇宙 V よりも真に大きくないのならば、 フォン・ノイマン宇宙 V つまり ZFC内で全て済むはずだ ところが、代数幾何や圏論のためには、フォン・ノイマン宇宙 V つまり ZFC内では狭く ZFC+G（ZFCの拡張）を必要とするのでしょ？
(参考) https://en.wikipedia.org/wiki/Grothendieck_universe Grothendieck universe Grothendieck universes and inaccessible cardinals Since the existence of strongly inaccessible cardinals cannot be proved from the axioms of Zermelo–Fraenkel set theory (ZFC), the existence of universes other than the empty set and Vω cannot be proved from ZFC either. However, strongly inaccessible cardinals are on the lower end of the list of large cardinals; thus, most set theories that use large cardinals (such as "ZFC plus there is a measurable cardinal", "ZFC plus there are infinitely many Woodin cardinals") will prove that Grothendieck universes exist.
https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%A9%E3%82%B9_(%E9%9B%86%E5%90%88%E8%AB%96) クラス (集合論) 公理的集合論におけるクラス ZFではクラスの概念を定式化することはできないので、クラスはメタ言語による同値な言明で置き換えることで扱うことになる。例えば、 AをZFを解釈する構造として、メタ言語での表現 {x ｜ x=x} の A における解釈は、 A の議論領域に属する要素全ての集まり（つまり、 A における集合すべての集まり）である。ゆえに、「全ての集合の成すクラス」を述語 x = xと（あるいはそれに同値な述語と）同一視することができる。
さあさ 始まるざますよ ”Spaces and perfectoids towards a perfectoid Siegel modular space” パーフィクトイド空間の紙芝居！ ；ｐ）
https://ahgt.math.cnrs.fr/activities/ateliers/AGA24-spaces%20perfectoid/ Arithmetic & Homotopic Galois Theory IRN Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ 2024 Spaces and perfectoids towards a perfectoid Siegel modular space July 19, 2024 · Paris & Japan [Bridge] · Org.: M. Ferreira-Filoramo (Sorbonne University), S. Philip (RIMS, Kyoto), N. Takada (Osaka University), N. Yamaguchi (Tokyo Institute of Technology, Tokyo) ＜google訳＞ パーフィクトイド空間の概念は、2012年にショルツによって導入されました。これは、p進ホッジ理論やラングランズ計画など、多くの強力な応用をすぐにもたらしました。2014年のBhattの言葉を引用すると、「パーフィクトイド空間の理論はかなり新しいものですが、すでに極めて強力です。これまでに発見された例のそれぞれのクラスは、数論幾何学における強力で深い定理につながっています。 」 パーフィクトイド空間のインスピレーションは、ガロア理論におけるフォンテーヌとウィンテンバーガーの古典的な結果、フーバー進空間、ベルコビッチ空間、テイトの剛体解析幾何学によって与えられた非アルキメデス空間上の解析幾何学の理論、およびゲーバーとラメロによって展開されたファルティングスの「ほとんど数学」の再統合から生まれました。
（まず、前振りで 望月IUT IVをば引用します） (望月新一ホームページ) LOG-VOLUME COMPUTATIONS AND SET-THEORETIC FOUNDATIONS Shinichi Mochizuki April 2020 P67 (抜粋) Section 3: Inter-universal Formalism: the Language of Species In the following discussion, we shall work with various models — consisting of “sets” and a relation “∈” — of the standard ZFC axioms of axiomatic set theory [i.e., the nine axioms of Zermelo-Fraenkel, together with the axiom of choice — cf., e.g., [Drk], Chapter 1, §3]. We shall refer to such models as ZFC-models. Recall that a (Grothendieck) universe V is a set satisfying the following axioms [cf. [McLn], p. 194]: (i) V is transitive, i.e., if y ∈ x, x ∈ V , theny ∈ V. (ii) The set of natural numbers N ∈ V. (iii) If x ∈ V, then the power set of x also belongs to V. (iv) If x ∈ V, then the union of all members of x also belongs to V. (v) If x ∈ V, y ⊆V,andf : x→y is a surjection, theny ∈ V. We shall say that a set E is a V-set if E ∈ V.
The various ZFC-models that we work with may be thought of as [but are not restricted to be!] the ZFC-models determined by various universes that are sets relative to some ambient ZFC-model which, in addition to the standard axioms of ZFC set theory, satisfies the following existence axiom [attributed to the “Grothendieck school” — cf. the discussion of [McLn], p. 193]: (†G) Given any set x, there exists a universe V such that x ∈ V. We shall refer to a ZFC-model that also satisfies this additional axiom of the Grothendieck school as a ZFCG-model. This existence axiom (†G) implies, in particular, that: Given a set I and a collection of universes Vi,wherei ∈ I, indexed by I [i.e., a ‘function’ I i→ Vi], there exists a [larger] universe V such that Vi ∈ V, fori ∈ I. 略 つづく
つづき Although we shall not discuss in detail here the quite difficult issue of whether or not there actually exist ZFCG-models, we remark in passing that it may be possible to justify the stance of ignoring such issues in the context of the present series of papers — at least from the point of view of establishing the validity of various “final results” that may be formulated in ZFC-models — by invoking the work of Feferman [cf. [Ffmn]]. Precise statements concerning such issues, however, lie beyond the scope of the present paper [as well as of the level of expertise of the author!]. ＜google部分訳＞ ZFCG モデルが実際に存在するかどうかという非常に難しい問題についてはここでは詳しく議論しませんが、この一連の論文の文脈では、少なくとも ZFC モデルで定式化される可能性のあるさまざまな「最終結果」の妥当性を確立するという観点からは、Feferman の研究 [cf. [Ffmn]] を引用することで、そのような問題を無視する立場を正当化できる可能性があることを付け加えておきます。ただし、そのような問題に関する正確な記述は、本論文の範囲を超えています [また、著者の専門知識のレベルを超えています]。 [McLn] S. MacLane, One Universe as a Foundation for Category Theory, Reports of the Midwest Category Seminar III, Lecture Notes in Mathematics 106, SpringerVerlag (1969). (引用終り)
補足 １）いまどき、普通は"宇宙"は、使わない 使う人は、"強制法"で使うくらい(圏論の土俵としてのグロタンディーク宇宙はあるが) ２）さて、"強制法"の歴史を見ると、ポール・コーエンの「1962年、連続体仮説と選択公理のZFからの独立性を証明」 その後、ソロヴェイ (1970)が 実数の集合のルベーグ可測性について論じている 「Shelah (1984) では到達不能基数の無矛盾性が、実数集合が全てルベーグ可測であるモデルの構成に必要であることが示された」 ３）つまり、ポール・コーエンの1962年から Shelah 1984年"強制法"の発展があって いまどきは "宇宙"と言えば、基礎論の"強制法"で使われるくらい ４）なので、"強制法"を知らない人が 数学用語"宇宙"を語ると 時代遅れの感あり 実際、望月氏が上げている [McLn]S. MacLane, One Universe as a Foundation for Category Theory, Reports of the Midwest Category Seminar III, Lecture Notes in Mathematics 106, SpringerVerlag (1969) で かなり古い 現代的な"宇宙"(2024)と整合しているかどうかが問題 それに、"One Universe as a Foundation for Category Theory" 宇宙は１つ "宇宙と宇宙をつなぐ" どっから出てきた？ｗ
>>867 >— at least from the point of view of establishing the validity of various “final results” that may be formulated in ZFC-models — by invoking the work of Feferman [cf. [Ffmn]]. >[Ffmn] S. Feferman, Set-theoretical Foundations of Category Theory, Reports of the Midwest Category Seminar III, Lecture Notes in Mathematics 106, SpringerVerlag (1969), pp. 201-247.
S. Feferman:ソロモン・フェファーマン（Solomon Feferman) フィールズ賞の チャールズ・ルイス・フェファーマン（Charles Louis Feffermanとは、別人ですね
Since the existence of strongly inaccessible cardinals cannot be proved from the axioms of Zermelo–Fraenkel set theory (ZFC), the existence of universes other than the empty set and V_ω cannot be proved from ZFC either. However, strongly inaccessible cardinals are on the lower end of the list of large cardinals; thus, most set theories that use large cardinals (such as "ZFC plus there is a measurable cardinal", "ZFC plus there are infinitely many Woodin cardinals") will prove that Grothendieck universes exist.
>>882 英語読める？ "ZFC plus there is a measurable cardinal" "ZFC plus there are infinitely many Woodin cardinals" はどちらもZFCじゃないよ 分かる？ 選択公理も分からんで数セミ記事が間違ってるとか トンデモ発言わめきちらしてる集合論ド素人君
>"ZFC plus there is a measurable cardinal" >"ZFC plus there are infinitely many Woodin cardinals" >はどちらもZFCじゃないよ 分かる？
君は基礎論ド素人だね
1）上記は グロタンディーク宇宙 ja.wikipedia.org/wiki/%E3%82%B0%E3%83%AD%E3%82%BF%E3%83%B3%E3%83%87%E3%82%A3%E3%83%BC%E3%82%AF%E5%AE%87%E5%AE%99 ここの「グロタンディーク宇宙と到達不能基数」に書いてあることじゃん 2）そして en.wikipedia.org/wiki/Grothendieck_universe ”Since the existence of strongly inaccessible cardinals cannot be proved from the axioms of Zermelo–Fraenkel set theory (ZFC), the existence of universes other than the empty set and V_ω cannot be proved from ZFC either. However, strongly inaccessible cardinals are on the lower end of the list of large cardinals; thus, most set theories that use large cardinals (such as "ZFC plus there is a measurable cardinal", "ZFC plus there are infinitely many Woodin cardinals") will prove that Grothendieck universes exist.” とあるよね ；ｐ） 3）"ZFC plus there is a measurable cardinal"の”measurable cardinal"にリンクがあるでしょ en.wikipedia.org/wiki/Measurable_cardinal だよ （google訳）「実数値の測定可能な基数の弱い到達不可能性」の項目に記載があるよ 4）”Woodin cardinal”についても en.wikipedia.org/wiki/Woodin_cardinal ”An equivalent definition is this: λ is Woodin if and only if λ is strongly inaccessible and for all A ⊆V_λ there exists a λA<λ which is <λ- A-strong.” とあるでしょ
” measurable cardinal"と”Woodin cardinal”のどちらも、到達不可能 or inaccessible である基数です ところで、君は到達不能基数が分ってないみたいだね ｗ ；ｐ）
[AS] U. Angehrn, Y.-T. Siu, Effective freeness and point separation for adjoint bundles, Invent. Math. 122 (1995), no. 2, 291–308.
[E] I. Enoki, Kawamata–Viehweg vanishing theorem for compact K¨ahler manifolds, Einstein metrics and Yang-Mills connections (Sanda, 1990), 59–68, Lecture Notes in Pure and Appl. Math., 145, Dekker, New York, 1993.
[O] T. Ohsawa, On a curvature condition that implies a cohomology injectivity theorem of Koll´arSkoda type, Publ. Res. Inst. Math. Sci. 41 (2005), no. 3, 565–577. [OT] T. Ohsawa, K. Takegoshi, On the extension of L2 holomorphic functions, Math. Z. 195 (1987), no. 2, 197–204.
[Tg] K. Takegoshi, Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper K¨ahler morphisms, Math. Ann. 303 (1995), no. 3, 389–416. (引用終り) 以上
https://mathoverflow.net/questions/142937/motivation-for-multiplier-ideal-sheaves motivation for multiplier ideal sheaves asked Sep 23, 2013 at 8:26 Koushik What is the origin of multiplier ideal sheaves? It was introduced ny Nadel.Yum Tong Siu,his advisor in his plenary lecture in 2002 icm mentions some thing that it arose in pde.Can anyone kindly elaborate on the motivation behind defining multiplier ideal sheaves. I think there are lots of experts here in mathoverflow who are experts in these things like diverio and many others. www-fourier.ujf-grenoble.fr/~demailly/manuscripts/trieste.pdf (Multiplier ideal sheaves and analytic methods in algebraic geometry Demailly, J.-P. (Universite de Grenoble I, Institut Fourier, Saint-Martin d'Heres (France)), E-mail: demailly@fourier.ujf-grenoble.fr Vanishing theorems and effective results in algebraic geometry 2001) this is I think one of the most standard places to learn about it. 回答略
https://www.kurims.kyoto-u.ac.jp/~yuichiro/talks.html 星 裕一郎 講演 https://sem-wnt.w.waseda.jp/ https://sem-wnt.w.waseda.jp/20240719.pdf 早稲田大学整数論セミナーの予定(2024年度 第7回) 日時：2024 年 7 月19 日（金）17:00～18:30 場所：早稲田大学西早稲田キャンパス 対面と Zoom ミーティングによるハイブリッド開催 講演者：星裕一郎氏（京都大学数理解析研究所） タイトル：Onthe Geometricity of Adelic Galois Sections of Hyperbolic Curves アブストラクト： A Galois section of a hyperbolic curve over a field is defined to be a continuous section of the natural continuous surjective outer homomorphism from the etale fundamental group of the given curve to the absolute Galois group of the basefield. Grothendieck’s section conjecture states that, for a given hyperbolic curve over a number field, an arbitrary Galois section of the curve is geometric, i.e., the image of an arbitrary Galois section of the curve is contained in a decomposition subgroup associated to a closed point of the curve. After a brief state of the background, this talk will report on recent and future developments concerning this conjecture. In particular, I will explain a proof of the geometricity of an adelic Galois section of a “sufficiently small” hyperbolic curve over a number field. Moreover, the final portion will report on some expected developments concerning this research via inter-universal Teichmuller theory. This talk is based on a joint work with Shinichi Mochizuki. 1
www.genealogy.math.ndsu.nodak.edu/id.php?id=268483 Shigeo Nakano MathSciNet Student: Name School Year Descendants Ohsawa, Takeo Kyoto University 1981 8
2次元ブレイドの研究も順調に進み、チャート表示法や4次元Alexander-Markov定理ができた。その研究を介して、J. Scott Carter教授、斎藤昌彦教授との交流が始まった。 彼らとの共同研究でカンドルのホモロジー理論という新しい数学を構築するに至った。 松本堯生教授、松本幸夫教授、Roger Fenn 教授との出会いは4次元レフシェツ束空間やバイカンドルの研究に繋がった。 このように出会いがきっかけとなり新たな研究がスタートする、研究を進めていくとまた新たな出会いがある。これが私の研究スタイルのようだ。
文献 [1] Jeffrey Weeks, The Shape of Space, Marcel Dekker, Inc., New York, 1985. [2] Akio Kawauchi, Tetsuo Shibuya, Sin’inchi Suzuki, Descriptions on surfaces in 4-space, Math. Sem. Notes Kobe Univ. 10 (1983), 75-125. [3] Seiichi Kamada, Non-orientable surfaces in 4-space, Osaka J. Math. 26 (1989), 367-385. (引用終り) 以上
https://ja.wikipedia.org/wiki/%E5%90%8D%E5%8F%A4%E5%B1%8B%E5%B8%82%E7%AB%8B%E5%A4%A7%E5%AD%A6 名古屋市立大学（なごやしりつだいがく、英語: Nagoya City University, NCU）は、愛知県名古屋市瑞穂区瑞穂町字川澄1番地に本部を置く日本の公立大学である。創立は1884年設置の名古屋薬学校が起源。1950年大学設置。略称は名市大（めいしだい）、市大（しだい）。 []
