Conference "Arithmetic, Geometry and Coding Theory"

March 14 - 18, 2011

CIRM, Marseille, France

Organisers: Yves Aubry (Université de la Méditerranée, IML), Christophe Ritzenthaler (Université de la Méditerranée, IML), Alexey Zykin (Mathematical Department of HSE, Laboratoire Poncelet, IITP)

Ranks of abelian varieties in towers of function fields

Yuri Zarhin

Abstract

We discuss explicit examples of abelian varieties of bounded rank in infinite towers of function elds of characteristic zero. In many cases we are able to compute the rank at every layer of the tower. This is a report on a joint work with Douglas Ulmer

Web page of the conference at CIRM