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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929: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2020/01/03(金) 19:51:56.43 ID:ivt0JCXh

>>888
＞ 2020年度、数理研では、宇宙際タイヒミューラー理論を中心的なテーマとした「訪問滞在型研究」＝通称「プロジェクト」（英語で説明するときは「スペシャル・イヤー」と呼ぶこともあります）が予定されており、
＞ 4件の大きな集会と、多数の海外からの訪問者により、以前にも増して多忙を極める一年になりそうです。これまでは関係者の大変な努力によって宇宙際タイヒミューラー理論の習熟者を一人ずつ育ててきており、
＞その数も10名に迫る勢いですが、今年はこれまで蓄積された知恵や、「よくある誤解」を効率よく処理する技術を総動員して、そのような習熟者を量産できる体制を確立していきたいと考えています。

IUTその４をざっと眺めてみた（＾＾；
１）
”the ABC Conjecture, and the Szpiro Conjecture for elliptic
curves all follow as special cases of Theorem A. ”
みんな、Theorem Aで証明可能？（＾＾

http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf
[4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. PDF 　　NEW !! (2019-10-31)

P3
Theorem A. (Diophantine Inequalities)
Then, relative to the notation of [GenEll]
[reviewed in the discussion preceding Corollary 2.2 of the present paper], one has
an inequality of “bounded discrepancy classes”
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 for
hyperbolic curves, the ABC Conjecture, and the Szpiro Conjecture for elliptic
curves all follow as special cases of Theorem A. We refer to [Vjt] for a detailed
exposition of these conjecture

つづく

http://rio2016.5ch.net/test/read.cgi/math/1573769803/929

930: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2020/01/03(金) 19:55:42.47 ID:ivt0JCXh

>>929

つづき
２）
Corollary 2.3. (Diophantine Inequalities) と、Theorem A. (Diophantine Inequalities) は、ほぼ同じか

P54
Corollary 2.3. (Diophantine Inequalities)

P55
Remark 2.3.1. We take this opportunity to correct some unfortunate misprints
in [GenEll].

P63
Remark 2.3.4. Various aspects of the theory of the present series of papers
are substantially reminiscent of the theory surrounding Bogomolov’s proof of
the geometric version of the Szpiro Conjecture, as discussed in [ABKP], [Zh].
Put another way, these aspects of the theory of the present series of papers may
be thought of as arithmetic analogues of the geometric theory surrounding Bogomolov’s proof. Alternatively, Bogomolov’s proof may be thought of as a sort of
useful elementary guide, or blueprint [perhaps even a sort of Rosetta stone!],
for understanding substantial portions of the theory of the present series of papers.
The author would like to express his gratitude to Ivan Fesenko for bringing to his
attention, via numerous discussions in person, e-mails, and skype conversations
between December 2014 and January 2015, the possibility of the existence of such
fascinating connections between Bogomolov’s proof and the theory of the present
series of papers. We discuss these analogies in more detail in [BogIUT].

つづく

http://rio2016.5ch.net/test/read.cgi/math/1573769803/930

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