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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116653Our 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.Number TheoryAlgebraic Geometry14G05, 11G40Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fieldstext