English

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.

Keywords

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}
}