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.
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
Lombardo D.;
2021-01-01
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.File in questo prodotto:
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