メモ
下記の”Appendix F. Uchida Trick”がちょっと面白いね

（参考）
https://www.uvm.edu/~tdupuy/papers.html
https://www.dropbox.com/s/7e7roesnirjxxlh/tables-only-live.pdf?
BASIC INTERPRETATIONS USED IN IUT
DRAFT
TAYLOR DUPUY

Abstract. This document contains a number of interpretation tables used in Mochizuki's
IUT papers. It is stripped from the Appendix of [DH20].

Appendix F. Uchida Trick
In what follows we let X be a smooth geometrically irreducible curve over a p-adic field
K which is of strictly Belyi type. We denote its function field by (X). Using structures
interpretable in 1(X) we show how to reconstuct the field K.
The construction is given below in the Figure 1.

Figure 1. A picture of the divisor and functions for the Uchida trick. In the
notation of this appendix P = P1;Q = P2;R = P3, a = λ, b = μ, f = f1 and
g = F2.

関連
https://www.math.upenn.edu/~pop/Research/files-Res/AnabPhen_20Dec10.pdf
Lectures on Anabelian Phenomena in Geometry and Arithmetic
Florian Pop, University of Pennsylvania
P3
This lead Neukirch to the following questions:
1) Does GQ have inner automorphisms only?
2) Is every isomorphism Φ : GK → GL as above defined by the conjugation by some element inside GQ ?
Finally, the first peak in this development was reached at the beginning of the
1970’s, with a positive answer to Question 1) by Ikeda [Ik] (and partial results by
Komatsu), and the break through by Uchida [U1], [U2], [U3] (and unpublished
notes by Iwasawa) showing that the answer to Question 2) is positive. Even
more, the following holds: