21/01/10 09:33:42.01 1u/qgB/5.net
メモ、よく纏まっている
（参考）
URLﾘﾝｸ(blog.livedoor.jp)
【数学】ABC予想ニュース【最新情報】2018年01月24日
宇宙際タイヒミュラー理論のまとめWiki Powered by ライブドアブログ
（上記より）
URLﾘﾝｸ(people.maths.ox.ac.uk)
Brief superficial remarks on Shinichi Mochizuki’s Interuniversal Teichmueller Theory
(IUTT), version 3 (27/12/2015)
Minhyong Kim
(抜粋)
1. Arithmetic elliptic curves in general position (AECGP): a height inequality in an
ideal case
2. Simulation of the subgroup A
3. Estimating arithmetic degrees
After these difficulties are dealt with, my impression is
that one ends up therefore with something like a ‘degree map with indeterminacies,’ (the ‘procession
normalised mono-analytic log volume’) which however can be precisely controlled. The inequality
between the arithmetic degree of
log q = (log(q1/(2l)v))v
and the possible arithmetic degrees of the log-equivariant
log Θ(x) = (log kΘ(x)kv)v
is the main concern of IUTT III, and is analysed using the interaction between the vertical log
direction and the horizontal theta direction of the two-dimensional lattice. The theta direction, by
the way, is a sophisticated version of the evaluation map on theta functions.
Mohamed Saidi has stressed to me that the inquality in IUTT III is not Szpiro’s inequality per se.
Rather, what is proved is the slightly curious statement that whenever a constant CΘ satisfies
-| log Θ| <= CΘ| log q|,
then CΘ >= -1. Then, in IUTT IV, a specific CΘ, involving h(E), the discriminant of the field, and
various other simple numbers, is shown to satisfy this inequality. For that specific choice, CΘ >= -1
is Szpiro’s inequality.