Algebraic Dynamics: Torsion points of elliptic curves via Berkovich spaces over Z

ALGEBRAIC DYNAMICS, SEMINARS

Speaker:

Jerome Poineau - Universite de Caen

Berkovich spaces over Z may be seen as fibrations containing complex analytic spaces as well as p-adic analytic spaces, for every prime number p. We will give an introduction to those spaces and explain how they may be used in an arithmetic context to prove height inequalities. As an application, following a strategy by DeMarco-Krieger-Ye, we will give a proof of a conjecture of Bogomolov-Fu-Tschinkel on uniform bounds on the number of common images on P^1 of torsion points of two elliptic curves.