Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
Our goal in this note is to give a number of examples of abelian varieties over function fields k(t) which have bounded ranks in towers of extensions such as k(t^{1/d}) for varying d. Along the way we prove some new results on Fermat curves which may be of independent interest.
Cite
@article{arxiv.math/0609716,
title = {Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields},
author = {Douglas Ulmer},
journal= {arXiv preprint arXiv:math/0609716},
year = {2007}
}