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Article Dans Une Revue Transactions of the American Mathematical Society, Series B Année : 2018

Chow motives associated to certain algebraic Hecke characters

Résumé

Shimura and Taniyama proved that if A is a potentially CM abelian variety over a number field F with CM by a field K linearly disjoint from F, then there is an algebraic Hecke character λ A of F K such that L(A/F, s) = L(λ A , s). We consider a certain converse to their result. Namely, let A be a potentially CM abelian variety appearing as a factor of the Jacobian of a curve of the form y e = γx f + δ. Fix positive integers a and n such that n/2 < a ≤ n. Under mild conditions on e, f, γ, δ, we construct a Chow motive M , defined over F = Q(γ, δ), such that L(M/F, s) and L(λ a A λ n−a A , s) have the same Euler factors outside finitely many primes.
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hal-03965642 , version 1 (31-01-2023)

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Laure Flapan, Jaclyn Lang. Chow motives associated to certain algebraic Hecke characters. Transactions of the American Mathematical Society, Series B, 2018, 5, pp.102-124. ⟨10.1090/btran/27⟩. ⟨hal-03965642⟩
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