現代数学の系譜工学物理雑談古典ガロア理論も読む79

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む79 (1002ﾚｽ)
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323: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/12/07(土) 16:24:59.86 ID:H2e5WMAT

>>306 補足
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
INTER-UNIVERSAL TEICHMULLER THEORY IV:LOG-VOLUME COMPUTATIONS AND SET-THEORETIC FOUNDATIONS Shinichi Mochizuki October 2019
(抜粋)
P3
Theorem A. (Diophantine Inequalities)

Thus, Theorem A asserts an inequality concerning the canonical height [i.e.,“htωX(D)”], the logarithmic different [i.e., “log-diffX”], and the logarithmic conductor [i.e., “log-condD”] of points of the curve UX valued in number fields whose extension degree over Q is ? d .
In particular,
the so-called Vojta Conjecture forhyperbolic curves,
the ABC Conjecture,
and the Szpiro Conjecture for elliptic curves
all follow as special cases of Theorem A.

P54
Corollary 2.3. (Diophantine Inequalities)

P57
Remark 2.3.3. Corollary 2.3 may be thought of as an effective version of the Mordell Conjecture.
From this point of view, it is perhaps of interest to compare the “essential ingredients” that are applied in the proof of Corollary 2.3 [i.e., in effect, that are applied in the present series of papers!] with the “essential ingredients” applied in [Falt].
The following discussion benefited substantially from numerous e-mail and skype exchanges with Ivan Fesenko during the summer of 2015.
(引用終り)

Vojta Conjecture forhyperbolic curves、ABC Conjecture、Szpiro Conjecture for elliptic curves、an effective version of the Mordell Conjecture
全部IUTの射程内だという
本当なら、面白いじゃない？ｗ（＾＾

http://rio2016.5ch.net/test/read.cgi/math/1573769803/323

354: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/12/11(水) 17:07:48.34 ID:W0aIOzhV

>>347
>IUTを発展させるためにも、しっかりと日本数学会で議論を
>だめならだめで良いじゃない
>中途半端が一番いけない

まあ、例えば、数学科生、M生、Dr生から見た時に
Vojta、Szpiro、effective version of the Mordell
（Conjecture）たちが、どうなっているだってこと

はっきりしてやれよ、日本数学会としてさ
（これから勉強ないし研究する方としては、はっきりしないの困るよね）

白ならベスト
真っ黒なら、ワーストだけど、まあそれも仕方ない
灰色なら、それもありだろうけど、どこまで分かって、ここがまだすっきりしないとか

現状をしっかりまとめて、情報発信すること
それを、４のWorkshopと連携してやれば良いんじゃね？

https://ja.yourpedia.org/wiki/%E5%AE%87%E5%AE%99%E9%9A%9B%E3%82%BF%E3%82%A4%E3%83%92%E3%83%9F%E3%83%A5%E3%83%A9%E3%83%BC%E7%90%86%E8%AB%96
宇宙際タイヒミュラー理論

(>>306)
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
INTER-UNIVERSAL TEICHMULLER THEORY IV: ¨
LOG-VOLUME COMPUTATIONS AND
SET-THEORETIC FOUNDATIONS
Shinichi Mochizuki
October 2019
Abstract.
(抜粋)
n the present paper, estimates arising from these multiradial algorithms for splitting monoids of LGP-monoids are applied to verify various diophantine results which imply,
for instance,
the so-called Vojta Conjecture for hyperbolic curves,
the ABC Conjecture,
nd the Szpiro Conjecture for elliptic curves.

（>>323）
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
INTER-UNIVERSAL TEICHMULLER THEORY IV:LOG-VOLUME COMPUTATIONS AND SET-THEORETIC FOUNDATIONS Shinichi Mochizuki October 2019
(抜粋)
P57
Remark 2.3.3. Corollary 2.3 may be thought of as an effective version of the Mordell Conjecture.

http://rio2016.5ch.net/test/read.cgi/math/1573769803/354

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