Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.