Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields
Douglas Ulmer
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(t1/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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