Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB

Taylor Dupuy; Kiran Kedlaya; David Roe; Christelle Vincent

paper

Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB

arXiv:2003.05380

Abstract

This document is intended to summarize the theory and methods behind fq_isog collection inside the ab_var database in the LMFDB as well as some observations gleaned from these databases. This collection consists of tables of Weil q-polynomials, which by the Honda-Tate theorem are in bijection with isogeny classes of abelian varieties over finite fields.

66 pages, 13 figures, 21 tables