# Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms

@article{Costa2019IdentifyingCE,
title={Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms},
author={Edgar Costa and D. Lombardo and J. Voight},
journal={arXiv: Number Theory},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Number Theory
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.
1 Citations
Determining monodromy groups of abelian varieties
Associated to an abelian variety over a number field are several interesting and related groups: the motivic Galois group, the Mumford-Tate group, $\ell$-adic monodromy groups, and the Sato-TateExpand

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