Kirti Joshi氏が、なかなか面白い仕事をしている
望月IUTをヒントに、さらに
望月IUTを、超えていこうとしているね
そして、自分の理論の楕円曲線論への応用を論じている

https://arxiv.org/pdf/2106.11452.pdf
Construction of Arithmetic Teichmuller Spaces and
some applications
Preliminary version for comments
Kirti Joshi
June 23, 2021

1 Introduction
§ 1.1 In this note I construct some categories which can be called Arithmetic Teichmuller
Spaces. This construction is very broadly inspired by Shinichi Mochizuki’s ideas on Anabelian
Geometry, p-adic Teichmuller theory and his work on the abc-conjecture, but my approach is
based on a completely different set of ideas.
Starting with any geometrically connected, smooth, quasi-projective variety X/L over number field L,
I show that there is a natural category, with a very rich structure, which can be called
an Arithmetic Teichmuller Space which is a product of categories J(X, Lp) for each non-trivial
valuation p of L (properties of J(X, Lp) are summarized in § 1.4), associated to the variety. My
construction works in any dimension and the category I construct also comes equipped with
functors to Mochizuki’s anabelian landscape (here the dimension is one).

つづく