L Anabelian geometry and IUT theory of Shinichi Mochizuki, and applications K 2d adelic analysis and geometry, and applications J Adelic structures on arithmetic and geometric surfaces, and applications I Higher integration, harmonic analysis and zeta integrals
B Class field theories, one-dimensional and higher dimensional 0125１３２人目の素数さん2021/12/29(水) 18:42:56.02ID:BG85dKWg>>72>>74の間が抜けていたので補足 908 名前:１３２人目の素数さん [sage] :2021/12/28(火) 20:56:41.90 ID:IQKnQwAx >>906 つづき
P74 Remark 3.3.1. (i) One well-known consequence of the axiom of foundation of axiomatic set theory is the assertion that “∈-loops” a ∈ b ∈ c ∈ ... ∈ a can never occur in the set theory in which one works. On the other hand, there are many situations in mathematics in which one wishes to somehow “identify” mathematical objects that arise at higher levels of the ∈-structure of the set theory under consideration with mathematical objects that arise at lower levels of this ∈-structure.
P75 That is to say, the mathematical objects at both higher and lower levels of the ∈-structure constitute examples of the same mathematical notion of a “set”, so that one may consider “bijections of sets” between those sets without violating the axiom of foundation. In some sense, the notion of a species may be thought of as a natural extension of this observation. That is to say, the notion of a “species” allows one to consider, for instance, speciesisomorphisms between species-objects that occur at different levels of the ∈-structure of the set theory under consideration - i.e., roughly speaking, to “simulate ∈-loops” - without violating the axiom of foundation. 0126１３２人目の素数さん2021/12/29(水) 18:43:03.66ID:BG85dKWg That is to say, the mathematical objects at both higher and lower levels of the ∈-structure constitute examples of the same mathematical notion of a “set”, so that one may consider “bijections of sets” between those sets without violating the axiom of foundation. In some sense, the notion of a species may be thought of as a natural extension of this observation. That is to say, the notion of a “species” allows one to consider, for instance, speciesisomorphisms between species-objects that occur at different levels of the ∈-structure of the set theory under consideration - i.e., roughly speaking, to “simulate ∈-loops” - without violating the axiom of foundation. 以上 0127１３２人目の素数さん2021/12/29(水) 18:44:07.76ID:BG85dKWg > 私を天羽優子氏と思ってるならそれ妄想ですから
・Como School “Unifying themes in Geometry”, September 27-30 2021 https://utge.lakecomoschool.org/ Unifying Themes In Geometry Lake Como School of Advanced Studies, 27 - 30 September 2021
Organizers and school lecturers Olivia Caramello (University of Insubria and IHES) Ivan Fesenko (University of Nottingham) Laurent Lafforgue (Huawei)
Supporting lecturers Wojciech Porowski (University of Nottingham)
Invited speakers Alain Connes (IHES) Misha Gromov (IHES and Courant Institute, N.Y.) Maxim Kontsevich (IHES) Barry Mazur (Harvard University)
Sponsors We gratefully acknowledge the support of the Lake Como School of Advanced Studies, the University of Insubria and the EPSRC Programme Grant Symmetries and Correspondences. 0141１３２人目の素数さん2021/12/29(水) 19:02:39.02ID:BG85dKWg キチガイジおばさんの症状 ・朝鮮人連呼(>>133)と日本人批判(>>131)の両極端にブレる…境界性人格障害症状 ・誰も興味を持たない狂人の素性や性別について言わなくていい言い訳をくどくどとする(>>123>>137)…自己愛性人格障害症状 0142１３２人目の素数さん2021/12/29(水) 19:04:24.04ID:BG85dKWg キチガイジおばさんの症状2 ・誰も興味のない狂人の同性愛の嗜好について余計な説明を試みる(>>139)…自己愛性人格障害症状 0143１３２人目の素数さん2021/12/29(水) 19:07:19.87>>140 programmeの英文が全く読めなかったようですね
Wojciech Porowski: “Introduction to anabelian geometry” [slides available here; video available here]
Abstract:
After recalling the notion of the étale fundamental group of a scheme, we will discuss how various properties of a hyperbolic curve can be reconstructed from its fundamental group. 0144１３２人目の素数さん2021/12/29(水) 19:08:52.69ID:lfES2Ayi 今回のサンプル a_watcher発狂の流れが面白過ぎる これは永久保存決定w
https://utge.lakecomoschool.org/programme/ Ivan Fesenko: “Higher adelic theory” [slides available here; video available here] Abstract: This talk starts a series of lectures on higher adelic theory (HAT) in the case of arithmetic surfaces and its applications. 2D objects associated to the surfaces and two different adelic structures on the surfaces will be introduced. The use of analytic adelic structures in higher zeta integrals and applications will be presented. The talk will start with the origin of several key developments in modern number theory: class field theory and its generalisations. https://www.dropbox.com/s/u4n8070t6s526ad/FesenkoSlides.pdf?dl=0 slides available here Ivan Fesenko: “Higher adelic theory”20210927 0149１３２人目の素数さん2021/12/29(水) 19:43:10.80ID:XncdaMzv>>140 まさに語るに落ちるというやつだ その研究集会でFesenkoはIUTの位置づけについて少々触れた程度で abcについては一切何も語らず、 IUTの詳細はRIMS集会の記録と引き続くPorowski氏の講演に押し付けてる それを受けたPorowskiの講演ではIUTガン無視で存在しないかのようだった IUTのオワコン感ハンパない 0150１３２人目の素数さん2021/12/29(水) 20:25:46.43ID:EeC8ikNf>>72なんだけども、前スレでホッジ理論に注意すべきだと書いたのは、確かこのループの話の動機付けが まさにホッジ理論の一般化にあると記憶していたからです ですが、このスレにはその問題を気にするレスが見当たりませんでした
https://ivanfesenko.org/wp-content/uploads/2021/10/prad-1.html Ivan Fesenko Higher adelic theory Como School, September 27 2021 36 / 37 List of open problems in HAT Selected open problems in 2d adelic analysis and geometry (updated December 2018) (D stands for ‘done’, P stands for ‘in progress’) 40 problems, 6 done, 9 partially done
Porowski氏は、上記は https://www.dropbox.com/s/kuiz1n7sqdggj9x/PorowskiSlides.pdf?dl=0 で、 （ここのP19のBelyi cuspidalization (2)の図は、まさにIUTのアニメの図でしょ（ https://www.kurims.kyoto-u.ac.jp/~motizuki/project-2021-japanese.html 宇宙際タイヒミューラー理論の拡がり ） それから、P30 References (2) で more detailed presentation として、Oxford IUT workshop, December 2015, slides by J. Stix, Kyoto IUT workshop, July 2016, slides by K. Higashiyama の二つを挙げている ） Porowski氏の下記 Overview of IUT theory 今読むと、絶品ですね。分かり易いわ。Porowski氏は優秀だね
（>>4より） https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/ExpHorizIUT21-IUTSummit-notes.html Inter-universal Teichmuller Theory (IUT) Summit 2021, RIMS workshop, September 7 - September 10 2021 Notes and recordings of the workshop
https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/documents/Fesenko%20-%20IUT%20and%20modern%20number%20theory.pdf van Fesenko IUT and modern number theory.
https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/documents/Porowski%20-%20Overview%20of%20IUT.pdf Wojciech Porowski Overview of IUT theory
因みに、南出明示公式は下記 https://www.kurims.kyoto-u.ac.jp/~motizuki/ExpHorizIUT21/WS4/documents/Minamide%20-%20Explicit%20Estimate.pdf Arata Minamide Explicit Estimates in Inter-universal Teichmuller Theory I and II, Reference: [ExpEst]. 0171１３２人目の素数さん2021/12/30(木) 00:10:35.66ID:En9CqBVW>>169 >フェセンコのHigher adelicて >せいぜい2次元なのかツマらんな
(参考) https://en.wikipedia.org/wiki/Class_field_theory#Generalizations_of_class_field_theory Class field theory Generalizations of class field theory There are three main generalizations, each of great interest. They are: the Langlands program, anabelian geometry, and higher class field theory. Often, the Langlands correspondence is viewed as a nonabelian class field theory. If and when it is fully established, it would contain a certain theory of nonabelian Galois extensions of global fields. However, the Langlands correspondence does not include as much arithmetical information about finite Galois extensions as class field theory does in the abelian case. It also does not include an analog of the existence theorem in class field theory: the concept of class fields is absent in the Langlands correspondence. There are several other nonabelian theories, local and global, which provide alternatives to the Langlands correspondence point of view.
Another generalization of class field theory is anabelian geometry, which studies algorithms to restore the original object (e.g. a number field or a hyperbolic curve over it) from the knowledge of its full absolute Galois group or algebraic fundamental group. Another natural generalization is higher class field theory, divided into higher local class field theory and higher global class field theory. It describes abelian extensions of higher local fields and higher global fields. The latter come as function fields of schemes of finite type over integers and their appropriate localizations and completions. It uses algebraic K-theory, and appropriate Milnor K-groups generalize the {\displaystyle K_{1}}K_{1} used in one-dimensional class field theory 0172１３２人目の素数さん2021/12/30(木) 07:45:26.44ID:En9CqBVW>>171 追加
https://en.wikipedia.org/wiki/Anabelian_geometry Anabelian geometry More recently, Mochizuki introduced and developed a so called mono-anabelian geometry which restores, for a certain class of hyperbolic curves over number fields or some other fields, the curve from its algebraic fundamental group. Key results of mono-anabelian geometry were published in Mochizuki's "Topics in Absolute Anabelian Geometry." Anabelian geometry can be viewed as one of generalizations of class field theory. Unlike two other generalizations ? abelian higher class field theory and representation theoretic Langlands program ? anabelian geometry is highly non-linear and non-abelian.
https://en.wikipedia.org/wiki/Higher_local_field Higher local class field theory Higher local class field theory is compatible with class field theory at the residue field level, using the border map of Milnor K-theory to create a commutative diagram involving the reciprocity map on the level of the field and the residue field.[7] General higher local class field theory was developed by Kazuya Kato[8] and by Ivan Fesenko.[9][10] (引用終り)
Higher local class field theory ”General higher local class field theory was developed by Kazuya Kato[8] and by Ivan Fesenko.[9][10]”ね Ivan Fesenko.出てくるね
Como Schoolの Porowskiの講演は、IUTの基礎の遠アーベルの部分で、講演自身ではIUTに触れてない>>148 だが、”P30 References (2) で more detailed presentation として、Oxford IUT workshop, December 2015, slides by J. Stix, Kyoto IUT workshop, July 2016, slides by K. Higashiyama の二つを挙げている”>>170 ことからすると
話の流れで、読む順は Como Schoolの Porowskiの講演 → IUT Summit Overview of IUT theory >>170 かも
この類のルサンチマンのこもったマウント発言を始終繰り返す下等生物はどこへ行っても相手にされない 0205１３２人目の素数さん2021/12/30(木) 10:03:21.57>>201 >出してくる文献が古過ぎるやん 仕方ないですよ 昭和時代末期の話ですからね >圏論プログラミング Lambek, J. and Scott, P. J., 1986. Introduction to Higher Order Categorical Logic, Cambridge University Press. という本は大学の図書館で見ましたよ まあ読まなかったんですけど
学部の時読んだのは、これですか David Gries The Science of Programming 0206１３２人目の素数さん2021/12/30(木) 10:05:10.28ID:4jYBn4KQ このID無しの話はどれも幼稚な聞き齧りと能書き垂れとマウントばかりで、いったい何年前から匿名掲示板廃人をやっているのか疑問を感じる 0207１３２人目の素数さん2021/12/30(木) 10:07:46.22ID:4jYBn4KQ 書き込みに脈絡がなく、話のテーマがコロコロ変わって安定しない所から見て、精神分裂症を患って長年廃人状態なのだろう
