An equivalent condition for abelian varieties over finite fields to have QM
Number Theory
2023-11-21 v1
Abstract
In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism algebras of abelian varieties over finite fields with Yu's criterion of the existence of homomorphisms between semi-simple algebras.
Keywords
Cite
@article{arxiv.2311.11051,
title = {An equivalent condition for abelian varieties over finite fields to have QM},
author = {Keisuke Arai and Yuuki Takai},
journal= {arXiv preprint arXiv:2311.11051},
year = {2023}
}
Comments
27 pages