Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB

Taylor Dupuy; Kiran Kedlaya; David Roe; Christelle Vincent

Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB

Number Theory 2020-09-24 v2

Authors: Taylor Dupuy , Kiran Kedlaya , David Roe , Christelle Vincent

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.

Keywords

abelian varieties finite fields isogeny classes weil q-polynomials honda-tate theorem lmfdb

Cite

@article{arxiv.2003.05380,
  title  = {Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB},
  author = {Taylor Dupuy and Kiran Kedlaya and David Roe and Christelle Vincent},
  journal= {arXiv preprint arXiv:2003.05380},
  year   = {2020}
}

Comments

66 pages, 13 figures, 21 tables

Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB

Abstract

Keywords

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