%0 Journal Article
%T Ranks of Jacobians in towers of function fields
%A Douglas Ulmer
%A Yuri G. Zarhin
%J Mathematics
%D 2010
%I arXiv
%X Let $k$ be a field of characteristic zero and let $K=k(t)$ be the rational function field over $k$. In this paper we combine a formula of Ulmer for ranks of certain Jacobians over $K$ with strong upper bounds on endomorphisms of Jacobians due to Zarhin to give many examples of higher dimensional, absolutely simple Jacobians over $k(t)$ with bounded rank in towers $k(t^{1/p^r})$. In many cases we are able to compute the rank at every layer of the tower.
%U http://arxiv.org/abs/1002.3318v2