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arXiv · 1906.02803

Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms

Edgar Costa·Davide Lombardo·John Voight
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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.

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Edgar Costa, Davide Lombardo, John Voight. 2020-10-26. Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms. https://arxiv.org/abs/1906.02803

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