Non-critical equivariant L-values of modular abelian varieties

Abstract : We prove an equivariant version of Beilinson's conjecture on non-critical L-values of strongly modular abelian varieties over number fields. The proof builds on Beilinson's theorem on modular curves as well as a modularity result for endomorphism algebras. As an application, we prove a weak version of Zagier's conjecture on L(E, 2) and Deninger's conjecture on L(E, 3) for non-CM strongly modular Q-curves.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01953036
Contributor : François Brunault <>
Submitted on : Wednesday, December 12, 2018 - 3:39:07 PM
Last modification on : Sunday, December 23, 2018 - 1:03:17 AM
Long-term archiving on : Wednesday, March 13, 2019 - 2:38:00 PM

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François Brunault. Non-critical equivariant L-values of modular abelian varieties. International Journal of Number Theory, World Scientific Publishing, 2018, 14 (09), pp.2517-2542. ⟨ensl-01953036⟩

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