Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
Number Theory
2020-10-27 v2
Abstract
Assuming the Mumford-Tate conjecture, we show that the center of the endomorphism ring of an abelian variety defined over a number field can be recovered from an appropriate intersection of the fields obtained from its Frobenius endomorphisms. We then apply this result to exhibit a practical algorithm to compute this center.
Keywords
Cite
@article{arxiv.1906.02803,
title = {Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms},
author = {Edgar Costa and Davide Lombardo and John Voight},
journal= {arXiv preprint arXiv:1906.02803},
year = {2020}
}
Comments
12 pages, minor revision