Non-critical equivariant L-values of modular abelian varieties

François Brunault (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Keywords: Modular abelian varieties; L-functions; Beilinson conjectures; Zagier's conjecture; Deninger's conjecture

Domains: Mathematics [math]; Mathematics [math]; Number Theory [math.NT]

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