IUTを読むための用語集資料集スレ

[過去ﾛｸﾞ] IUTを読むための用語集資料集スレ (1002ﾚｽ)
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552(2): 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 08:05:00.47 ID:V6fYxSC9(1/8) AAS
2chｽﾚ:math IUT と ABC予想 (応援スレ) 49
下記、Fig. 1 PDF中に図があるけど、IUT読む人は頭に入れておくのが良いと思う（＾＾
http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/documents/RIMS-Lille%20-%20Promenade%20in%20Inter-Universal%20Teichm%C3%BCller%20Theory.pdf
PROMENADE IN INTER-UNIVERSAL TEICHMULLER THEORY - 復元
Online Seminar - Algebraic & Arithmetic Geometry
Laboratoire Paul Painleve - Universite de Lille, France

P3
Modus Operandi & Leitfaden. As a new geometry, the essence of Mochizuki’s IUT is to introduce
a new semiotic system - formalism, terminology, and their interactions - that can be unsettling at first.
This programme proposes a 3 layers approach with precise references, examples, and analogies.
Because IUT discovery also benefits from a non-linear and spiralling approach, we provide further
indications for an independent wandering: Mochizuki recommends to start with the introductory [Alien] -
young arithmetic-geometers can also consult [Fes15] for a shorter overview. We also recommend to begin
with §Intro - §3.6-7 ibid. for a direct encounter with IUT’s semiotic, then to follow one’s own topics of
interest according to Fig. 1, which also indicates some topic-wise references as entry-points - [EtTh],
[GenEll], etc. Within the “canon” [IUTChI]-[IUTChIV], our recommendation is to start with [IUTChIII]
§Introduction. Intuition of the reader can further rely on the strongly consistent terminology of IUT -
e.g. Frobenioid, mono-anabelian transport, arithmetic analytic.

Fig. 1. IUT, Topics & References as potential entry points.
● Diophantine: Heights, Faltings’ isogenies & Abc.
● Anabelian: Mono-anabelian reconstruction & Tripodal transports.
● Geometry: Multiradiality, Coricity & Arithmetic Analyticity vs Holomorphicity.
● Categorical: Frobenioids, Anabelioid, Prime Strips & Hodge Theaters.
● Meta-Abelian 略
つづく

553: 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 08:05:38.83 ID:V6fYxSC9(2/8) AAS
>>552
つづき

※ We have also found the synthetic and selfcontent [Yam17] to be particularly helpful as a bridge between [Alien] and the “canon”.

※ Hodge-Arakelov and p-adic Teichmuller theories stand as important models for IUT, which also relies on key
categorical constructions - e.g. Frobenioids and anabelioids. These aspects are not included in this programme
- we refer to [Alien] and the canon for references - they can be the object of additional talks by specialists.
以上

554(1): 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 08:06:28.04 ID:V6fYxSC9(3/8) AAS
2chｽﾚ:math IUT と ABC予想 (応援スレ) 49

>※ We have also found the synthetic and selfcontent [Yam17] to be particularly helpful as a bridge between [Alien] and the “canon”.

“canon”：(正典) IUT論文1〜4 みたいだね（＾＾；

（参考）
https://ejje.weblio.jp/content/canon
canonとは weblio
主な意味
教会法、教会法令集、(倫理・芸術上の)規範、規準、(聖書外典に対して)正典

http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/documents/RIMS-Lille%20-%20Promenade%20in%20Inter-Universal%20Teichm%C3%BCller%20Theory.pdf
PROMENADE IN INTER-UNIVERSAL TEICHMULLER THEORY - 復元
Online Seminar - Algebraic & Arithmetic Geometry
Laboratoire Paul Painleve - Universite de Lille, France
(抜粋)
P2
※ In order to keep the length of this guide (incl. 〜 25 tables, figures, and diagrams) strictly shorter than the IUT corpus
- 〜 1200 pages with a piece of anabelian geometry, 〜 675 pages for the canon, and 〜 170 pages for the introductory [Alien]
- some details have been omitted, some approximations were made; they should be negligible for our goal. Content will be
updated according to the progress of the seminar, see version and date.

P3
Within the “canon” [IUTChI]-[IUTChIV], our recommendation is to start with [IUTChIII]
§Introduction. Intuition of the reader can further rely on the strongly consistent terminology of IUT -
e.g. Frobenioid, mono-anabelian transport, arithmetic analytic.

※ Hodge-Arakelov and p-adic Teichmuller theories stand as important models for IUT, which also relies on key
categorical constructions - e.g. Frobenioids and anabelioids. These aspects are not included in this programme
- we refer to [Alien] and the canon for references - they can be the object of additional talks by specialists.

つづく

555(1): 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 08:07:05.29 ID:V6fYxSC9(4/8) AAS
>>554
つづき
>※ We have also found the synthetic and selfcontent [Yam17] to be particularly helpful as a bridge between [Alien] and the “canon”.

そうか、この[Alien]っていうのが、重要な論文なんだね〜（＾＾
P4
[Alien]：
[Alien] S. Mochizuki, “The mathematics of mutually alien copies: From Gaussian integrals to Inter-universal
Teichmuller theory,” RIMS Preprint no. 1854, 169p. Jul. 2016, Eprint available on-line.

http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-japanese.html
望月論文

http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf
[7] The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory. PDF
　　NEW !! (2020-04-04)

Abstract
Inter-universal Teichm¨uller theory may be described as a construction of certain
canonical deformations of the ring structure of a number field
equipped with certain auxiliary data, which includes an elliptic curve over the number field
and a prime number ? 5. In the present paper, we survey this theory by focusing on the
rich analogies between this theory and the classical computation of the Gaussian integral.
The main common features that underlie these analogies may be summarized as follows:
・ the introduction of two mutually alien copies of the object of interest;
・ the computation of the effect -i.e., on the two mutually alien copies of the object of interest -of two-dimensional changes of coordinates by considering the effect on infinitesimals;

つづく

556: 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 08:07:21.50 ID:V6fYxSC9(5/8) AAS
>>555
つづき

・ the passage from planar cartesian to polar coordinates and the resulting splitting, or decoupling, into radial -i.e., in more abstract valuation-theoretic terminology, “value group” -and angular -i.e., in more abstract valuation-theoretic terminology, “unit group” -portions;
・ the straightforward evaluation of the radial portion by applying the quadraticity of the exponent of the Gaussian distribution;
・ the straightforward evaluation of the angular portion by considering the metric geometry of the group of units determined by a suitable version of the natural logarithm function.

[Here, the intended sense of the descriptive “alien” is that of its original Latin root, i.e., a
sense of abstract, tautological “otherness”.] After reviewing the classical computation
of the Gaussian integral, we give a detailed survey of inter-universal Teichm¨uller theory by
concentrating on the common features listed above. The paper concludes with a discussion
of various historical aspects of the mathematics that appears in inter-universal Teichm¨uller theory.
(引用終り)
以上

567(2): 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 21:57:20.81 ID:V6fYxSC9(6/8) AAS
>>563
>コピペの限界はオリジナルが間違っていてもそれに気が付かないということ……！

気付くとき多いし（過去スレ見れば分かるよ）
正しいと思ったものをコピペしているし
間違ったと思うなら、どうぞ、指摘すれば良いじゃん？（＾＾
それって、おれ以外のみんなに言えることでしょ

そもそもが、基本は５ｃｈって、名無しさんだからさ
「だれが言ったから正しい」なんてことはないのが原則だよ
何が正しいか、コピペであろうがなんであろうが、自分で判断するしかない
それが数学ってもんだろ？

IUTアンチは、自分の無能を棚に上げるから
困るｗ（＾＾；

568(1): 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 22:06:15.48 ID:V6fYxSC9(7/8) AAS
>>565-566
おサルのバカ頭には困ったものだな〜ｗ（＾＾
IUTが、お前に読めるのか？
あ〜んっ？ｗｗｗ

望月先生がIUT論文を2012年夏に発表した
その後、査読は2017年まで5年くらいかかったらしいが
2018年のSSと望月＆星の討論を経て、さらに２年追加検証されたという

プロ数学者が、IUT検証に５年かかる
何年か前だが、ブライアンコンラッドとキランケドラヤが（下記）、IUTが分からん・読めないと言っている（>>558の通り）
そんなものが、定義を読んだからと言って、なんだ？　どうした？　お前に読めるはずないでしょ！

もちろん、おれも読めないが
斜めには読むぜよｗ（＾＾
それについては、応援スレに書いているよ（ Inter-universal geometry と ABC予想 (応援スレ) 49 2chｽﾚ:math ）

いやね
おれも加藤文元本は読んだけど
ちょっとあれじゃね（＾＾

楕円曲線もなにも出てこないじゃん
スピロだって出てこない
ちょっとあれじゃね（＾＾；

そういう人
多いんじゃない？（＾＾

570: 現代数学の系譜雑談 ◆yH25M02vWFhP [] 2020/10/20(火) 23:38:46.08 ID:V6fYxSC9(8/8) AAS
別に指摘してくれとは言っていない
コピペしようが、コピペで無く自分の文章で書こうが同じだってことさ

はっきり言って、コピペで無く自分の文章で書こうが、
結局は５ｃｈに書かれることなんて
新規な数学概念なんてないでしょ、学会じゃないんだから

新規な数学概念や、新規な数学理論ではないということは
種本があるわけだわな
だったら、コピペしようが、コピペで無く自分の文章で書こうが同じだってことさ

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