望月Inter-universal Teichmuller theory (abbreviated as IUT) (下記)は、新しい局面に入りました。 査読が終り出版されました。また、“Explicit”版が公開され、査読は完了したようです。 IUTの4回の国際会議は無事終わり、Atsushi Shiho (Univ. Tokyo, Japan)先生が、参加したようです。 IUTが正しいことは、99%確定です。 このスレは、IUT応援スレとします。番号は前スレ43を継いでNo.44からの連番としています。 (なお、このスレは本体IUTスレの43からの分裂スレですが、実は 分裂したNo43スレの中では このスレ立ては最初だったのです!(^^;)
つづく https://twitter.com/5chan_nel (5ch newer account) 0003132人目の素数さん2022/05/28(土) 13:30:21.83ID:DzamZmOV <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
つづく 0008132人目の素数さん2022/05/28(土) 13:32:22.33ID:DzamZmOV 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 0014132人目の素数さん2022/05/28(土) 13:34:22.55ID:DzamZmOV つづき
(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 https://rio2016.5ch.net/test/read.cgi/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.
Classification of Riemann surfaces Parabolic Riemann surfaces If X is a Riemann surface whose universal cover is isomorphic to the complex plane C then it is isomorphic one of the following surfaces:
・ C itself; ・The quotient C/Z; ・A quotient C/(Z +Zτ) where τ ∈ C with Im (τ)>0. Topologically there are only three types: the plane, the cylinder and the torus. But while in the two former case the (parabolic) Riemann surface structure is unique, varying the parameter τ in the third case gives non-isomorphic Riemann surfaces. The description by the parameter τ gives the Teichmuller space of "marked" Riemann surfaces (in addition to the Riemann surface structure one adds the topological data of a "marking", which can be seen as a fixed homeomorphism to the torus). To obtain the analytic moduli space (forgetting the marking) one takes the quotient of Teichmuller space by the mapping class group. In this case it is the modular curve.
Hyperbolic Riemann surfaces In the remaining cases X is a hyperbolic Riemann surface, that is isomorphic to a quotient of the upper half-plane by a Fuchsian group (this is sometimes called a Fuchsian model for the surface). The topological type of X can be any orientable surface save the torus and sphere.
A case of particular interest is when X is compact. Then its topological type is described by its genus g>= 2. Its Teichmuller space and moduli space are 6g-6-dimensional. A similar classification of Riemann surfaces of finite type (that is homeomorphic to a closed surface minus a finite number of points) can be given. However in general the moduli space of Riemann surfaces of infinite topological type is too large to admit such a description.
Punctured spheres These statements are clarified by considering the type of a Riemann sphere C^ with a number of punctures. With no punctures, it is the Riemann sphere, which is elliptic. With one puncture, which can be placed at infinity, it is the complex plane, which is parabolic. With two punctures, it is the punctured plane or alternatively annulus or cylinder, which is parabolic. With three or more punctures, it is hyperbolic - compare pair of pants. One can map from one puncture to two, via the exponential map (which is entire and has an essential singularity at infinity, so not defined at infinity, and misses zero and infinity), but all maps from zero punctures to one or more, or one or two punctures to three or more are constant. (引用終り) 以上 0041132人目の素数さん2022/05/30(月) 21:31:59.35ID:ve96nUDX 順序数の引き算するアホに数学語る資格ないわ 0042132人目の素数さん2022/05/31(火) 01:20:22.25ID:tzKRVEL7 ソリトン理論=可積分系とか書いていたくせに、羞恥心もなく「格上げします」と。 論文をコネとか、本当にわかっていないね。 査読論文でも、ハゲタカ雑誌だとマイナス評価になる。 こういうのが政治家になると、ほんとうに害になる。 慎太郎のせいで都立大が劣化したけど、影響力が減ってきたら学部名を元にもどして正常化しようとしている。 0043132人目の素数さん2022/05/31(火) 03:00:11.71ID:RTL3hvmL>>38 >以前 昔基礎論やっていたと名乗っていたよ それ別人 0044132人目の素数さん2022/05/31(火) 03:10:32.51ID:RTL3hvmL ところで単位円板ΔってC-{0,1}の普遍被覆だよな? 0045132人目の素数さん2022/05/31(火) 12:38:14.27ID:MlKwzN+F>>44 複素平面CはC-{0}の普遍被覆 で被覆写像はexp 0046132人目の素数さん2022/05/31(火) 12:40:19.01ID:MlKwzN+F>>45 さて単位円板ΔからC-{0,1}への被覆写像は何でしょう? 0047132人目の素数さん2022/05/31(火) 15:38:23.69ID:WPtRs/LU>>46 具体的にかけるん? 0048132人目の素数さん2022/05/31(火) 16:09:55.17ID:vMcsOxZ+ λ関数とかね 金八(?)先生お得意 0049132人目の素数さん2022/05/31(火) 16:13:29.69ID:74gZ5LCo>>48 どんな関数ですか? ググッてもλ計算しか出てこない 0050132人目の素数さん2022/05/31(火) 16:57:25.55ID:Z5nIGKup>>49 モジュラーλ 0051132人目の素数さん2022/05/31(火) 18:10:36.17ID:ETK56POA>>50 thx 0052132人目の素数さん2022/05/31(火) 18:25:09.94ID:ETK56POA 上半平面で微分が消えないのはどうやって示すんですか? 0053132人目の素数さん2022/05/31(火) 18:37:31.38ID:ETK56POA あぁ、対数微分か なるほろ 0054132人目の素数さん2022/05/31(火) 20:58:30.75ID:Rwy4VmWC \Σ コン! コン!/ || ||Ю 0055132人目の素数さん2022/05/31(火) 20:59:50.72ID:Rwy4VmWC λッテモ ョロスィィ…デスカ? || / ||Ю 0056132人目の素数さん2022/05/31(火) 21:01:12.26ID:Rwy4VmWC 彡|| 彡|| ガチャッ! / 彡||Ю 0057132人目の素数さん2022/05/31(火) 21:03:15.85ID:Rwy4VmWC … || ∞ || ´д`)||Ю 0058132人目の素数さん2022/05/31(火) 21:05:45.40ID:Rwy4VmWC || ∞ || ダレカ ィマセンカ~? ´д`)||Ю 0059132人目の素数さん2022/05/31(火) 21:07:21.23ID:Rwy4VmWC || Σ∞ || マタªªズレマクッテルッピ! ;´д`)||Ю 0060132人目の素数さん2022/05/31(火) 21:08:34.81ID:Rwy4VmWC || ∞ || … ´д`)||Ю 0061132人目の素数さん2022/05/31(火) 21:09:08.39ID:Rwy4VmWC || ∞ || ダレモィナィッピ… ´д`)||Ю 0062132人目の素数さん2022/05/31(火) 21:10:14.97ID:Rwy4VmWC || ∞ || …ズレガ治ッテルッピ… ´д`)||Ю 0063132人目の素数さん2022/05/31(火) 21:11:05.77ID:Rwy4VmWC || ∞ || …コンナボッチスルルェヂャ ´д`)||Ю 0064132人目の素数さん2022/05/31(火) 21:13:14.51ID:Rwy4VmWC || ∞ || 太~ィ鬱ガλッチャ´~`ゥゥ… *´д`)||Ю 0065132人目の素数さん2022/05/31(火) 21:27:36.54ID:Rwy4VmWC ✨🌟✨
https://ivanfesenko.org/ News ? Ivan Fesenko https://ivanfesenko.org/?page_id=80 https://www.youtube.com/watch?v=OQG0OeQla1w Ivan Fesenko "Underlying deep properties of numbers" 725 回視聴 2022/02/20 I will talk about adelic and anabelian geometries whose use expands our understanding of discrete structures such as integer numbers and solutions of Diophantine equations Geometries underlying deep properties of numbers (on the IUT theory), video of a talk at Institute of Mathematics, Kyiv, Ukraine
Institute of Mathematics / ?нститут Математики 0072132人目の素数さん2022/06/02(木) 14:13:12.10ID:+tDJfbdT メモ
https://www.youtube.com/watch?v=ikalrqtLc5U Wojciech Porowski: “Introduction to anabelian geometry” 395 回視聴 2021/12/09 Wojciech Porowski: “Introduction to anabelian geometry”
After recalling the notion of the etale fundamental group of a scheme, we will discuss how various properties of a hyperbolic curve can be reconstructed from its fundamental group.
へー、そんなの読んでいるのか 私には、雲の上の話だね 下記”The mock theta functions in the notebook have been found to be useful for calculating the entropy of black holes.[4]” で、”mock theta”大栗先生が、何かで書いていたね 検索すると、下記が見つかった
Contents Rankin (1989) described the lost notebook in detail. The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics. The mock theta functions in the notebook have been found to be useful for calculating the entropy of black holes.[4]
References Bibliography Andrews, George E.; Berndt, Bruce C. (2012), Ramanujan's lost notebook. Part III, Berlin, New York: Springer-Verlag, ISBN 978-1-4614-3809-0