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)
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