(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments (参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Taylor Dupuy says: April 14, 2020 at 8:37 pm Yep, the theta pilot doesn’t map to the actual theta values *on the theta side*. On the q-side it does.
I will check your manuscript again in a bit. Dinner then bedtime (I am barbecuing).
I want to check again to make sure I didn’t miss something. 0074132人目の素数さん2020/04/15(水) 10:25:36.79ID:LTi2Xsr9>>73 訂正
ダブり一つ消す(^^; 0075132人目の素数さん2020/04/15(水) 11:46:43.32ID:LTi2Xsr9>>73 >”I will check your manuscript again in a bit. Dinner then bedtime (I am barbecuing).” >”barbecuing”は、バーベキューだね
Taylor Dupuy先生 いい味出しているね〜w(^^; バーベキューか
うまくいけば ここで決着するかもね
ショルツ先生が納得する形でね そう予想しておきますw(^^ 0076132人目の素数さん2020/04/15(水) 18:40:13.07ID:LTi2Xsr9>>73 Taylor Dupuy の長文レスが来た(^^; いやはや、面白いね〜w
2018年京都の議論が下敷きにあるから より踏み込んだ議論になっている気がするな〜w
一つ言えることは Taylor Dupuy 先生は、一歩も後退していないよね
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋)
Taylor Dupuy says: April 15, 2020 at 5:17 am 0077132人目の素数さん2020/04/15(水) 19:27:21.29ID:LqgT1sVr やっぱりショルツはやらかしちゃった感じだ? 奴が白旗を上げた時のキチガイアンチが見ものよな 0078現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/15(水) 22:25:24.82ID:Rsdt7V/S>>77 同意 そうかも知れないね まあ、私には、数学的な判断を直接下す能力はない
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Peter Scholze says: April 15, 2020 at 5:10 pm Dear UF (and Taylor and everyone),
I won’t comment any further here on statements of the form “well, maybe Mochizuki actually meant (vague statement)”.
A few comments up I summarized the situation with claims (1), (2) and (3). I have seen no valid objection to (1) and (2), and (2) alone would lead to a contradiction (as one gets too strong a form of ABC). To (3), Taylor indicated where to cut the diagram, but I really don’t think this is what happens, as this would isolate Theta-pilots from Theta-values and effectively remove the actual Theta-values from the proof; while Mochizuki does consider this “Theta-intertwining” which is the association of the Theta-pilot with the Theta-values.
I will only comment further here if either a valid objection to (1) or (2) is mentioned, or further clarification is given regarding (3). Any further technical discussions are probably best done via e-mail.
ここでは、「まあ、望月さんは実際には(曖昧な発言)という意味だったのかもしれませんが」という形の発言については、これ以上コメントしません。 (原文:I won’t comment any further here on statements of the form “well, maybe Mochizuki actually meant (vague statement)”.)
>>80 >ここでは、「まあ、望月さんは実際には(曖昧な発言)という意味だったのかもしれませんが」という形の発言については、これ以上コメントしません。 >(原文:I won’t comment any further here on statements of the form “well, maybe Mochizuki actually meant (vague statement)”.)
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit
UF says: April 15, 2020 at 9:11 pm @Peter Scholze: Thank you for your comments. Just to restate my view, in case I was unclear: I believe that the reasoning above for not including any specific identifications of the π1's (i.e. just full poly-isomorphisms) in the definition of the log-link is entirely parallel to Mochizukis reasoning in [IUT II, 1.11.2(ii)] for not including any specific identifications of the π1's in the definition of the theta-link.
deepl翻訳(一部修正あり) https://www.deepl.com/ja/translator コメントありがとうございます。 念のため、私の見解を述べさせていただきますと、(原文”believe”だから、「信じるところを述べると」でしょう) 上記の「π1の具体的な特定を含まない」という理由は、π1の (すなわち、just full poly-isomorphisms ですが) 対数リンクの定義において、完全に平行です 望月の理由付け [IUT II, 1.11.2(ii)]における(原文 to Mochizukis reasoning in [IUT II, 1.11.2(ii)] ) それは 含まない どんな 特定の π1の同定 シータリンクの定義に対して だからです。 (引用終り)
<補足> ”for not including any specific identifications of the π1's in the definition of the theta-link.” のところが、なかなか解釈が難しいが 「ショルツ氏のいうような、”any specific identifications of the π1's”は、”Mochizukis reasoning in [IUT II, 1.11.2(ii)] ”には、決して含まれない」 ってことなのでしょうね〜w
https://en.wikipedia.org/wiki/William_Thurston William Thurston (抜粋) To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important corollary is that many knots and links are in fact hyperbolic. Together with his hyperbolic Dehn surgery theorem, this showed that closed hyperbolic 3-manifolds existed in great abundance.
The geometrization theorem has been called Thurston's Monster Theorem, due to the length and difficulty of the proof. Complete proofs were not written up until almost 20 years later. The proof involves a number of deep and original insights which have linked many apparently disparate fields to 3-manifolds.
http://www.mathematik.uni-r.de/friedl/papers/dmv_091514.pdf THURSTON’S VISION AND THE VIRTUAL FIBERING THEOREM FOR 3-MANIFOLDS STEFAN FRIEDL (抜粋) Abstract. The vision and results of William Thurston (1946-2012) have shaped the theory of 3-dimensional manifolds for the last four decades. The high point was Perelman’s proof of Thurston’s Geometrization Conjecture which reduced 3- manifold topology for the most part to the study of hyperbolic 3-manifolds. In 1982 Thurston gave a list of 24 questions and challenges on hyperbolic 3-manifolds. The most daring one came to be known as the Virtual Fibering Conjecture. We will give some background for the conjecture and we will explain its precise content. We will then report on the recent proof of the conjecture by Ian Agol and Dani Wise.
The first major step towards a proof of the Geometrization Conjecture was Thurston’s ‘Monster Theorem’ from the late 1970s, namely the proof of the Geometrization Theorem for Haken manifolds. As we hinted at in the previous section, the proof uses an induction argument on hierarchies. But along the way Thurston also introduced a wealth of new concepts and ideas, many of which developed into major fields of study in their own right. William Thurston was awarded the Fields medal in 1983^8, but it took about 20 years and the efforts of many authors for all details to be written down rigorously. It is worth reading Thurston’s interesting argument [Th1994] why he did not provide the detailed proof himself. The full proof of the Geometrization Conjecture was finally given by Perelman [Pe2002, Pe2003a, Pe2003b] in 2003 using the Ricci flow on Riemannian metrics, building on ideas pioneered by Richard Hamilton [Ha1982].
>The geometrization theorem has been called Thurston's Monster Theorem, due to the length and difficulty of the proof. Complete proofs were not written up until almost 20 years later.
”William Thurston was awarded the Fields medal in 1983^8, but it took about 20 years and the efforts of many authors for all details to be written down rigorously. It is worth reading Thurston’s interesting argument [Th1994] why he did not provide the detailed proof himself.”
サーストンにとったら 怪物定理なんて 数ある業績のほんの一部ってことかもしれないがね(^^; 0096現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/17(金) 10:23:06.73ID:uc+pAU0w>>95 >”William Thurston was awarded the Fields medal in 1983^8,
(参考) https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A3%E3%83%BC%E3%83%AB%E3%82%BA%E8%B3%9E フィールズ賞 (抜粋) 1982年(ワルシャワ) ・アラン・コンヌ(Alain Connes, 1947年 - )フランスの旗 フランス 「 Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general. 」 ・ウィリアム・サーストン(William P. Thurston, 1946年 - 2012年)アメリカ合衆国の旗 アメリカ合衆国 「 Revolutionized study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. Contributed idea that a very large class of closed 3-manifolds carry a hyperbolic structure. 」 ・丘成桐(Shing-Tung Yau, 1949年 - )アメリカ合衆国の旗 アメリカ合衆国(中国系) 「 Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge-Ampere equations. 0097現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/17(金) 10:25:47.56ID:uc+pAU0w <転載> Inter-universal geometry と ABC 予想 43 https://rio2016.5ch.net/test/read.cgi/math/1577518389/212 212 名前:132人目の素数さん[] 投稿日:2020/04/16(木) 20:16:52.77 ID:2hTnrFrU [2/2] >>211 >数論幾何解らない連中の巣窟じゃ仕方無いだろ
I am an Assistant Professor at the Research Institute for Mathematical Sciences, Kyoto University. I have much interest in arithmetic geometry surrounding hyperbolic curves, especially anabelian geometry and its application. 7Papers and Preprints ・ On the Geometric Subgroups of the Etale Fundamental Groups of Varieties over Real Closed Fields (with Yuichiro Hoshi and Takahiro Murotani) RIMS Preprint 1910: (PDF).
・ Combinatorial Belyi Cuspidalization and Arithmetic Subquotients of the Grothendieck-Teichmuller Group RIMS Preprint 1899: (PDF)(Revisions) (PDF(Revised version)).
・ Geometric Version of the Grothendieck Conjecture for Universal Curves over Hurwitz Stacks RIMS Preprint 1886: (PDF).
・ Geometric Version of the Grothendieck Conjecture for Universal Curves over Hurwitz Stacks: a research announcement to appear in RIMS Kokyuroku Bessatsu: (PDF).
Educational History: ・2015 March: Graduated from the Department of Science of Kyoto University ・2017 March: Graduated from the Master Course of the Graduate School of Science of Kyoto University (under the supervision of Professor Shinichi Mochizuki) ・2020 March: Graduated from the Doctor Course of the Graduate School of Science of Kyoto University (under the supervision of Professor Shinichi Mochizuki) 0103132人目の素数さん2020/04/17(金) 11:56:59.39ID:HnGpk1CO コネ 0104現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/17(金) 12:03:00.70ID:uc+pAU0w>>103 コネ、大事だよ コネ、ウンも実力の内だよ (^^; 0105現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/17(金) 20:25:19.96ID:PJFvwFBv>>339 >学部2年までほとんど教養科目をやっている人間が
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Taylor Dupuy says: April 17, 2020 at 12:17 pm Hi Everyone, I’m just going to make one last post to close out some loose ends for interested readers. I also want to point out some things that we haven’t covered that I think are important. I’ve omitted the discussions of asymptotics of Mochizuki’s formula but other than that, I think I covered my IOUs. If there are any analytic number theorists who were really looking forward to that please email me. Sorry for the length. ********************** Regarding (3): Is Mochizuki’s Proof Falsified? ********************** There is no *proof* that Mochizuki’s method doesn’t work. The following is what the Scholze-Stix manuscript proves: 略
Peter Scholze says: April 17, 2020 at 6:25 pm Dear Taylor, thanks for these final comments! I think I should answer to this. Let me first say that I agree with much of what you write, and for the sake of keeping this short, I only jump at the few places where I disagree. > Regarding (3): Is Mochizuki’s Proof Falsified? […] > Finally, it is not outside the realm of reality that there could be 5 top notch international referees who have understood the proof as complete and correct.
Really? I would have hoped that in that case at least one of them ? not in their role as a referee, but simply as a mathematician who wants to share insight ? would have come around and explain the key ideas in a way that is understandable. 略 0109現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 09:34:37.05ID:FUrf+qJl>>108
まず、文字化け訂正
Really? I would have hoped that in that case at least one of them ? not in their role as a referee, but simply as a mathematician who wants to share insight ? would have come around and explain the key ideas in a way that is understandable. ↓ Really? I would have hoped that in that case at least one of them − not in their role as a referee, but simply as a mathematician who wants to share insight − would have come around and explain the key ideas in a way that is understandable.
さて Dupuy says ”Finally, it is not outside the realm of reality that there could be 5 top notch international referees who have understood the proof as complete and correct.”
かな そして、上記 Scholze氏発言(上記訂正の)”・・would have come around and explain the key ideas in a way that is understandable.” は、「RIMSよ、説明責任を果たせ!」ってことですね Scholze氏は、海外の数学者の多くを代表していると思います 「RIMSのやっていること、わけわからん、ごらぁ〜、ちゃんと説明しろ〜!」ってことです(^^; 0110現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 09:51:09.97ID:FUrf+qJl>>98 >数学科学部4年前期か通年かで
https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Taylor Dupuy says: April 17, 2020 at 12:17 pm ******************* Remarks on IUT3 3.11.i ******************* In the situation of (i) you lift to an richer stronger and more powerful structure that allows you to define (b) and (c) then then you stick them inside the log shell. What the proposition is saying is that this is well-defined up to ind1,2 ? so everything that was stuck inside these log shells now is considered up to a jumbling of the type described in a previous response. I will refer readers to my manuscripts with Anton Hilado for these formulas. (引用終り)
これ、多分 下記 1.The Statement of Mochizuki's Corollary 3.12, unstable preprint available on request, (with A. Hilado) だな (参考 >>36より) https://www.uvm.edu/~tdupuy/papers.html [ Taylor Dupuy's Homepage] (抜粋) 1.The Statement of Mochizuki's Corollary 3.12, unstable preprint available on request, (with A. Hilado) 2.Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12, (with A. Hilado) https://www.dropbox.com/s/hwdxtpk5ydqhp6g/thm1p10-short.pdf (引用終り)
なお、A. Hilado氏は、”Ph.D. student at the University of Vermont under Taylor Dupuy”で(下記) おそらくは、上記2つの論文”Mochizuki's Corollary 3.12”は、かれのDR論文ネタだ
(参考) https://ahilado.wordpress.com/about/ About My name is Anton Hilado. I am a mathematics Ph.D. student at the University of Vermont under Taylor Dupuy. 0112現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 10:11:18.32ID:FUrf+qJl>>111 タイポ訂正
その点、ショルツ先生は、説明 うまいな〜(^^ でも、どっかで嵌まっているのでしょうねぇ〜(^^; 0115現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 10:39:07.25ID:FUrf+qJl>>109 補足 >Really? I would have hoped that in that case at least one of them − not in their role as a referee, but simply as a mathematician who wants to share insight − would have come around and explain the key ideas in a way that is understandable.
https://ja.wikipedia.org/wiki/%E5%9C%8F_(%E6%95%B0%E5%AD%A6) 圏 (抜粋) 空間を圏で表す (O, <=) が順序集合のとき、これを次のような圏 CO と同一視することができる:obj(CO) = O とし、p, q ∈ O = obj(CO) について p <= q のとき、およびそのときに限り p から q への射がただ 1 つ存在する、として CO における射を定める ここで順序関係の推移律が射の合成に、反射律が恒等射に対応している。特に位相空間 X に対してその開集合系 O(X) を圏と見なすことができる G が群のとき、対象 Y ただ 1 つからなり、Hom (Y, Y) ≡ G であるような圏を G と同一視することができる。また、位相空間の基本亜群や「被覆」のホロノミー亜群など、様々な亜群による幾何学的な情報の定式化が得られている これらは様々な種類の数学的対象を圏によって言い換えていることになる。層やトポスの概念によってこれらを共通の文脈の中におくことが可能になる
Institut des Hautes Etudes Scientifiques (IHES) チャンネル登録者数 3.38万人 We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q_p and over F_p((t)) are equivalent, generalizing to the relative situation a theorem of Fontaine-Wintenberger, and also implying a strong form of Faltings's almost purity theorem. This method of changing the characteristic is then applied to deduce many cases of the weight-monodromy conjecture.
なお、References [Ho14] Y. Hoshi,、[Mo99] S. Mochizuki, が上がっているね(^^ [SGA4] M. Artin,; A. Grothendieck and J. L. Verdier,が導来圏の論文? 良く知らないのだが(^^;
(参考) https://arxiv.org/pdf/1504.01068.pdf Anabelian geometry with etale homotopy types ALEXANDER SCHMIDT AND JAKOB STIX Date: July 14, 2016. (抜粋) References [Ho14] Y. Hoshi, The Grothendieck conjecture for hyperbolic polycurves of lower dimension. J. Math. Sci. Univ. Tokyo 21 (2014), no. 2, 153?219. [Mo99] S. Mochizuki, The local pro-p anabelian geometry of curves. Invent. Math. 138 (1999), no. 2, 319?423. [SGA4] M. Artin,; A. Grothendieck and J. L. Verdier,Theorie des topos et cohomologie etale des schemas (SGA 4). Lecture Notes in Mathematics 269, 270 and 305, 1972/3. (引用終り)
(参考) https://en.wikipedia.org/wiki/Jakob_Stix Jakob Stix (抜粋) Jakob M. Stix (born in 1974) is a German mathematician. He deals with arithmetic algebraic geometry (etale fundamental group, anabelian geometry and others).
Stix studied mathematics in Freiburg and Bonn and received his doctorate in 2002 from Florian Pop at the University of Bonn (Projective Anabelian Curves in Positive Characteristic and Descent Theory for Log-Etale Covers[1]). 0120現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 12:44:50.40ID:FUrf+qJl>>119 JAKOB STIX arxiv "Anabelian geometry with etale homotopy types" References SGA1〜7 たしか、「佐藤の数学」に、柏原先生が 当時 GrothendieckのSGAなどを独学で読んで 佐藤超関数の基礎付け(特異コホモロジー論)に使って、論文を書いたとか
なので、IUTもそれなりに理解した上での記者会見であることは間違いないでしょう (少なくとも、2018年のSS vs 望月星 論争の報告書や関連文書には目を通して理解した上で、「望月の勝ち!」という判断をしたに違いないのです(^^; )
(参考) https://arxiv.org/pdf/1504.01068.pdf Anabelian geometry with etale homotopy types ALEXANDER SCHMIDT AND JAKOB STIX Date: July 14, 2016. (抜粋) References [SGA1] A. Grothendieck, Revetements etales et groupe fondamental, Lecture Notes in Mathematics 224, Springer-Verlag, Berlin, 1971. Seminaire de Geometrie Algebrique du Bois Marie 1960?1961 (SGA 1), Augmente de deux exposes de M. Raynaud. [SGA3] M. Demazure, A. Grothendieck, Schemas en groupes. II: Groupes de type multiplicatif, et structure des schemas en groupes generaux. Lecture Notes in Mathematics 152, Springer-Verlag, Berlin-New York, 1970, Seminaire de Geometrie Algebrique du Bois Marie 1962?64 (SGA 3), Dirige par M. Demazure et A. Grothendieck. [SGA4] M. Artin,; A. Grothendieck and J. L. Verdier,Theorie des topos et cohomologie etale des schemas (SGA 4)1972/3. [SGA4 1/2] P. Deligne, Cohomologie etale. Seminaire de Geometrie Algebrique du Bois-Marie SGA 4 1/2. Avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier. SpringerVerlag, Berlin-New York, 1977. [SGA7] Groupes de monodromie en geometrie algebrique. I. Seminaire de Geometrie Algebrique du Bois-Marie 1967?1969 (SGA 7 I). Dirige par A. Grothendieck. Springer-Verlag, Berlin-New York, 1972. 0121現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 13:04:34.84ID:FUrf+qJl>>120 追加
脚注 9^ Perfectoid spaces: A survey, to appear in Proceedings of the 2012 conference on Current Developments in Mathematics.
http://www.math.uni-bonn.de/people/scholze/CDM.pdf PERFECTOID SPACES: A SURVEY 1This work was done while the author was a Clay Research Fellow. PETER SCHOLZE Abstract. This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as complements to the results of the previous papers.
Contents 1. Introduction 2 2. Perfectoid Spaces 3 2.1. Introduction 3 2.2. Some open questions 9 3. p-adic Hodge theory 13 3.1. Introduction 13 3.2. A comparison result for constructible coefficients 17 3.3. The Hodge-Tate spectral sequence 20 4. A p-adic analogue of Riemann’s classification of complex abelian varieties 25 4.1. Riemann’s theorem 25 4.2. The Hodge-Tate sequence for abelian varieties and p-divisible groups 26 4.3. A p-adic analogue: The Hodge-theoretic perspective 29 4.4. A p-adic analogue: The geometric perspective 30 5. Rapoport-Zink spaces 32 6. Shimura varieties, and completed cohomology 36 References 37 0123132人目の素数さん2020/04/18(土) 13:14:02.93ID:UOshm4Zs 過疎 0124現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 13:33:53.71ID:FUrf+qJl>>122 追加
http://www.mars.dti.ne.jp/~kshara/haracv.html Keisuke Hara, Ph.D.(Math.Sci.) (抜粋) Degrees: B.A.(Pure and Applied Science) , March 1991, University of Tokyo, Japan. M.A.(Mathematical Science), March 1993,Graduate School of Mathematical Science, University of Tokyo, Japan. Ph.D.(Mathematical Science), March 1996, Graduate School of Mathematical Science, University of Tokyo, Japan.
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Peter Scholze says: April 17, 2020 at 7:15 pm PS: I just realized that maybe the following information is worth sharing. Namely, as an outsider one may wonder that the questions being discussed at length in these comments (e.g., the issue of distinct copies etc.) are very far from the extremely intricate definitions in Mochizuki’s manuscripts (his notation is famously forbidding, some of it surfaced in Taylor’s comments), and feel almost philosophical, so one might wonder that one is not looking at the heart of the matter.
However, the discussions in Kyoto went along extremely similar lines, and these discussions were actually very much led, certainly initially, by Mochizuki. He first wanted to carefully explain the need for distinct copies, by way of perfections of rings, and then of the log-link, leading to discussions rather close to the one I was having with UF here. He agreed that one first has to understand these basic points before it makes sense to introduce all further layers of complexity. (I should add that we did also go through the substance of the papers, but kept getting back at how this reflects on the basic points, as we all agreed that this is the key of the matter.) 0132132人目の素数さん2020/04/18(土) 21:19:36.58ID:DH+1jv2r Scholze賢者タイムw 0133現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/18(土) 21:24:32.42ID:FUrf+qJl>>119 >JAKOB STIX さんの方が >IUTについては、ショルツ氏より知識は上でしょうね >しかし、JAKOB STIX氏の声が聞こえてこない >いま、どう思っているのかな?
https://www.math.columbia.edu/~woit/wordpress/?p=11723 Not Even Wrong Why the Szpiro Conjecture is Still a Conjecture Posted on April 18, 2020 by woit
OP says: April 18, 2020 at 4:41 pm The comment of @naf hits the nail on the head. But I would go a step further: when confronted with a truly massive edifice of highly technical mathematics, nearly all experts need some kind of motivation to persevere beyond the final goal at the end of the tunnel. For example, a powerful heuristic to give confidence in the strategy, or some kind of intuitive guide to grab onto along the way to have a feeling of making progress (or at least interesting achievements along the way in the absence of a global guide). But here there is nothing of the sort, not even a compelling mathematical reason to believe at the outset that investing a huge amount of time is going to reap satisfying mathematical understanding. There is only patience to keep oneself going, and it can be very hard to rely on that alone after a lot of time.
This practical (albeit psychological) concern came to mind almost immediately after I was asked early on to be on the referee team for the IUT papers. I have great respect for Mochizuki’s mathematical talent, and no doubt in the sincerity of his belief that he has a proof of the main result. But I could see that the referees would not only have to check the details of an extremely long work written in a very obscure style (which didn’t provide insightful reasons for confidence in the approach being used). They would also have to engage in a herculean effort to get the writing substantially changed. It was too much, so I declined and communicated my concerns to the editorial board. (I recommended immediate rejection with a demand that the work be completely rewritten before it could be reconsidered.)
I am very sorry to see all these years later that neither the referees who were eventually obtained nor the editorial board obtained any real improvement on the clarity of the way the material is presented, not even at least an Introduction presenting key new insights in some conventional manner (to compensate for the way the technical material is presented). I hope the editors of PRIMS and the senior faculty at RIMS will reflect on their responsibility to the field of mathematics, and reconsider what they are doing. (引用終り) 以上 0139現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/19(日) 09:06:41.26ID:ijGx7lvx>>138 DeepL翻訳(一部修正)
ということは、海外の数学者では、「IUT訳分からん。RIMS訳分からん」という人多数でしょうね まあ、別スレで、ショルツ氏が納得すれば、ともかくも RIMS側が説明責任を果たす努力を怠ってはいけないと思う 0142現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/19(日) 09:56:50.80ID:ijGx7lvx>>131 Taylor Dupuy先生、いい味だしているね〜w(^^
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Taylor Dupuy says: April 18, 2020 at 1:09 pm Hi Everyone,
もう1つ 「サーストンのモンスター定理(ハーケン多様体には幾何構造が入る)」(>>143&>>95) これは、もっとひどくってw(^^; (>>95) ”William Thurston was awarded the Fields medal in 1983^8, but it took about 20 years and the efforts of many authors for all details to be written down rigorously. It is worth reading Thurston’s interesting argument [Th1994] why he did not provide the detailed proof himself.” つまり、サーストン先生自身は定理の証明を書かずに ”about 20 years and the efforts of many authors for all details to be written down rigorously.” というから、まあ米国の佐藤幹夫先生みたいなものかw
説明の何百ページの文書はいらないんだ ただ、「国際会議でちゃんと説明するから」くらいでいいんだ あるいは、もし国際会議用に準備している文書があるから、それを先にリリースして 「国際会議で議論予定」でもいいけどね 0147現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/19(日) 11:37:59.79ID:ijGx7lvx>>145 追加 https://www.math.columbia.edu/~woit/wordpress/?p=11723 Not Even Wrong Why the Szpiro Conjecture is Still a Conjecture Posted on April 18, 2020 by woit (抜粋) OP says: April 18, 2020 at 8:49 pm Just to clarify: I wasn’t a referee on the IUT papers, but rather was invited to serve as one, and I declined (giving the editorial board my recommendation for how I thought would be best to proceed). As for Katz’ work as a referee on the initial FLT paper, my impression is that this only became public knowledge sometime after the fix was found and the corrected version had gone through the review process (e.g., maybe via the BBC video that was made about it).
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit W says: April 19, 2020 at 9:53 am 0156132人目の素数さん2020/04/20(月) 13:14:27.34ID:nSShSe+M ΘとかΘ±ell とか D-Θ±ell ってどう翻訳すればいいんだろうな? 0157現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/20(月) 13:22:03.00ID:jS1N2Wjo>>136 >IUT論文において、サーストン怪物定理の図8(>>95)みたいなの >これが欲しいね
そうそう 追加で 1.IUT用語辞書 or 定義集(含む本論文ページへのヒモつけ) 2.インデックス(上記と重なる部分あるが、しっかり整備要。用語のみならず、数学記号も) 3.IUT用語と標準数学用語との対比表(差分を表示)(上記と重なる部分もあるが、しっかり整備すること)
そこはアブストラクトじゃんかw(^^; で http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf INTER-UNIVERSAL TEICHMULLER THEORY I: CONSTRUCTION OF HODGE THEATERS Shinichi Mochizuki April 2020 P6 In some sense, the main goal of the present paper may be thought of as the construction of Θ±ell NF-Hodge theaters [cf. Definition 6.13, (i)] P7 one may associate a D-Θ±ell NF-Hodge theater [cf. Definition 6.13, (ii)] (引用終り)
結論:この文書には "Θ±ell"の詳しい記載なし
そこで、下記山下先生のレビューが役に立つのです〜(^^ これ、IUTの前の準備文書が含まれているから、調べるのに便利だということに気付いたのです http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2019Jul5.pdf A PROOF OF THE ABC CONJECTURE AFTER MOCHIZUKI By Go Yamashita preprint. last updated on 8/July/2019. (注意:文字化けがあるので、必ず原文見て下さい!) P14 We write M ell ⊂ M ell ̄ for the fine moduli stack of elliptic curves and its canonical compactification.
結論:これより、ell:elliptic curve です
P199 § 10. Hodge Theatres. In this section, we construct Hodge theatres after fixing an initial Θ-data (Section 10.1). More precisely, we construct Θ±ell NF-Hodge theatres (In this survey, we shall refer to them as ◇□-Hodge theatres). A Θ±ellNF-Hodge theatre (or a ◇□-Hodge theatre) will be obtained by “gluing” (Section 10.6) ・a ΘNF-Hodge theatre, which has a F*l-symmetry, is related to a number field, of arithmetic nature, and is used to Kummer theory for NF (In this survey, we shall refer to it as a -Hodge theatre, Section 10.4) and
P200 ・a Θ±ell-Hodge theatre, which has a F x±-symmetry, is related to an elliptic curve, of geometric nature, and is used to Kummer theory for Θ (In this survey, we shall refer to it as a -Hodge theatre, Section 10.5) Separating the multiplicative (◇) symmetry and the additive (□) symmetry is also important (cf. [IUTchII, Remark 4.7.3, Remark 4.7.6]). ΘNF-Hodge theatre F*l-symmetry (◇) arithmetic nature Kummer theory for NF Θ±ell-Hodge theatre Fx±l-symmetry (□) geometric nature Kummer theory for Θ
結論: "Θ±ell"で、 Θは Θ-data (Section 10.1). 分かったのはここまで 多分、§ 10. Hodge Theatres. をもう少し読み込めば、±の意味( + and - か、あるいは + or - か、多分前者と思う)などはっきりすると思う NFも、Kummer theory for NF とあるので、もう少し読み込めば、はっきりすると思うけどね
https://books.google.co.jp/books?id=81QeCwAAQBAJ&printsec=frontcover&dq=Teichmuller+Mochizuki&hl=ja&sa=X&ved=0ahUKEwjR3tP7hffoAhVPPnAKHVZeDbIQ6AEIKDAA#v=onepage&q=Teichmuller%20Mochizuki&f=false Foundations of p-adic Teichmuller Theory 著者: Shinichi Mochizuki ASM 1999 0173現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 07:44:51.24ID:/78llOaT>>170 訂正と追加 訂正 >>167はすぐその下とダブりで消す
追加 "NF"について 下記P12 the abbreviations NF for "number field" ですね(^^ http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2019Jul5.pdf A PROOF OF THE ABC CONJECTURE AFTER MOCHIZUKI By Go Yamashita preprint. last updated on 8/July/2019. (注意:文字化けがあるので、必ず原文見て下さい!) P12 Number Fields and Local Fields: In this survey, we define a number field to be a finite extension of Q (i.e., we exclude infinite extensions). We define a mixed characteristic (or non-Archimedean) local field to be a finite extension of Qp for some p. We use the abbreviations NF for "number field", MLF for "mixed characteristic local field", and CAF for "complex Archimedean field" (i.e., a topological field isomorphic to C). For a topological field k which is isomorphic to R or C, we write j _ jk : k ! R>=0 for the absolute value associated to k, i.e., the unique continuous map such that the restriction of j_jk to k determines a homomorphism k ! R>0 with respect to the multiplicative structures of k and R>0, and jnjk = n for n ∈ Z>=0. We write π ∈ R for the mathematical constant pi (i.e., π = 3:14159 ・ ・ ・ ). (引用終り)