IUTを読むための用語集資料集スレ

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554: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/10/20(火) 08:06:28.04 ID:V6fYxSC9

https://rio2016.5ch.net/test/read.cgi/math/1600350445/541 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

http://rio2016.5ch.net/test/read.cgi/math/1592654877/554

555: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/10/20(火) 08:07:05.29 ID:V6fYxSC9

>>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

http://rio2016.5ch.net/test/read.cgi/math/1592654877/555

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