On the Birch and Swinnerton-Dyer conjecture for abelian varieties attached to Hilbert modular forms

DOI10.1016/j.jnt.2010.11.008zbMath1226.11070OpenAlexW2094017441WikidataQ122872734 ScholiaQ122872734MaRDI QIDQ627627

Cristian Virdol

Publication date: 3 March 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.11.008

zbMATH Keywords

abelian varietyHilbert modular formsBirch and Swinnerton-Dyer conjecturetotally real number field

Mathematics Subject Classification ID

Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Zeta functions and (L)-functions of number fields (11R42) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Totally real fields (11R80)

Related Items (3)

The critical values of \(L\)-functions of CM-base change for Hilbert modular forms ⋮ ON THE SPECIAL VALUES OF L-FUNCTIONS OF CM-BASE CHANGE FOR HILBERT MODULAR FORMS ⋮ On the critical values of \(L\)-functions of base change for Hilbert modular forms. II

Cites Work

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• On Galois representations associated to Hilbert modular forms
• On the Birch-Swinnerton-Dyer quotients modulo squares
• Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties
• Potential automorphy and change of weight
• On the arithmetic of abelian varieties
• Heights of Heegner points on Shimura curves.

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