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

2006/09/26 by Douglas Ulmer, Ulmer, Douglas
Computer Science · Mathematics · #11G40 #14G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0609716

openalex publication_date 2006/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

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