Non-critical equivariant L-values of modular abelian varieties

François Brunault

doi:10.1142/S1793042118501506

Non-critical equivariant L-values of modular abelian varieties

Number Theory 2023-06-23 v2 Algebraic Geometry

Authors: François Brunault

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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. 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 $\mathbf{Q}$ -curves.

Keywords

equivariant beilinson conjecture non-critical l-values modular abelian varieties number fields zagier's conjecture deninger's conjecture q-curves

Cite

@article{arxiv.1402.4495,
  title  = {Non-critical equivariant L-values of modular abelian varieties},
  author = {François Brunault},
  journal= {arXiv preprint arXiv:1402.4495},
  year   = {2023}
}

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18 pages

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