Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields

Details Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields

2006-09-26

arxiv.org/abs/math/0609716v1

Mathematics

Number Theory

Scientific paper

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.

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