Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
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classification
math.NT
keywords
endomorphismsabeliancenterfrobeniusvarietyalgorithmapplyappropriate
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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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