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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
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