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• W3087407610 abstract "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–Tate group. Assuming the Mumford–Tate conjecture, we show that from two well chosen Frobenius polynomials of our abelian variety, we can recover the identity component of these groups (or at least an inner form), up to isomorphism, along with their natural representations. We also obtain a practical probabilistic algorithm to compute these groups by considering more and more Frobenius polynomials; the groups are connected and reductive and thus can be expressed in terms of root datum. These groups are conjecturally linked with algebraic cycles and in particular we obtain a probabilistic algorithm to compute the dimension of the Hodge classes of our abelian variety for any fixed degree." @default.
• W3087407610 created "2020-09-25" @default.
• W3087407610 creator A5013166421 @default.
• W3087407610 date "2022-10-12" @default.
• W3087407610 modified "2023-10-16" @default.
• W3087407610 title "Determining monodromy groups of abelian varieties" @default.
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• W3087407610 doi "https://doi.org/10.1007/s40993-022-00391-0" @default.
• W3087407610 hasPublicationYear "2022" @default.
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