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Journal Articles International Journal of Number Theory Year : 2018

Non-critical equivariant L-values of modular abelian varieties

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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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Dates and versions

ensl-01953036 , version 1 (12-12-2018)

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  • HAL Id : ensl-01953036 , version 1

Cite

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