Inter-universal geometry と ABC予想 49

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 49 (1002ﾚｽ)
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942: 2020/04/14(火)23:30 ID:mIlcNUlX(7/7) AA×
>>930

ID:TosO5VR6
外部ﾘﾝｸ:en.wikipedia.org
外部ﾘﾝｸ[pdf]:pdfs.semanticscholar.org
外部ﾘﾝｸ:ja.wikipedia.org

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942:  [sage] 2020/04/14(火) 23:30:54.56 ID:mIlcNUlX

>>930 ｗ（＾＾；

ID:TosO5VR6さん
>Remark5の何が間違ってるかわからないorz
>スタンダードなファルティングスの有限性定理そのものだと思うけど
>望月反論ペーパー読んだら納得いきました
>「ごめんなさい。ファルティングスの証明を理解していませんでした」なんて、プライドもあって言えないだろうし

これね（＾＾；
（参考）
https://en.wikipedia.org/wiki/Faltings%27s_theorem
Faltings's theorem
(抜粋)
In arithmetic geometry, the Mordell conjecture is the conjecture made by Mordell (1922) that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points. In 1983 it was proved by Gerd Faltings (1983, 1984), and is now known as Faltings's theorem.
The conjecture was later generalized by replacing Q by any number field.

Proofs
Faltings (1983) proved the Shafarevich finiteness conjecture using a known reduction to a case of the Tate conjecture, and a number of tools from algebraic geometry, including the theory of Neron models.
The main idea of Faltings' proof is the comparison of Faltings heights and naive heights via Siegel modular varieties.[1]

Later proofs
A proof based on diophantine approximation was given by Vojta (1991). A more elementary variant of Vojta's proof was given by Bombieri (1990).

Generalizations
Even more general conjectures have been put forth by Paul Vojta.

Footnotes
1^ "Faltings relates the two notions of height by means of the Siegel moduli space.... It is the main idea of the proof." Bloch, Spencer (1984).
https://pdfs.semanticscholar.org/b509/4b4b6f31976173c38813428be512f7d35c9c.pdf
"The Proof of the Mordell Conjecture" (PDF). The Mathematical Intelligencer. 6 (2): 44.

https://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A1%E3%83%AB%E3%83%86%E3%82%A3%E3%83%B3%E3%82%B0%E3%82%B9%E3%81%AE%E5%AE%9A%E7%90%86
ファルティングスの定理

http://rio2016.5ch.net/test/read.cgi/math/1586650355/942

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