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

Douglas Ulmer
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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.

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Douglas Ulmer. 2006-09-26. Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields. https://arxiv.org/abs/math/0609716

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