Diophantine geometry and Serre C*-algebras

Igor Nikolaev

Published 2020-09-03Version 1

Let $V(k)$ be projective variety over a number field $k$ and let $K$ be a finite extension of $k$. We classify the $K$-isomorphisms of $V(k)$ in terms of the Serre $C^*$-algebra of $V(k)$. As an application, a new proof of the Faltings Finiteness Theorem for the rational points on the higher genus curves is suggested.