Functiones et Approximatio Commentarii Mathematici

Base change and the Birch and Swinnerton-Dyer conjecture

Cristian Virdol

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Abstract

In this paper we prove that if the Birch and Swinnerton-Dyer conjecture holds for products of abelian varieties attached to Hilbert newforms of parallel weight 2 with trivial central character, then the Birch and Swinnerton-Dyer conjecture holds for products of abelian varieties attached to Hilbert newforms of parallel weight 2 with trivial central character regarded over arbitrary totally real number fields.

Article information

Source
Funct. Approx. Comment. Math., Volume 46, Number 2 (2012), 189-194.

Dates
First available in Project Euclid: 25 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.facm/1340628401

Digital Object Identifier
doi:10.7169/facm/2012.46.2.4

Mathematical Reviews number (MathSciNet)
MR2931665

Zentralblatt MATH identifier
1298.11062

Subjects
Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Secondary: 11F80: Galois representations 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R80: Totally real fields [See also 12J15] 11G05: Elliptic curves over global fields [See also 14H52]

Keywords
Birch and Swinnerton-Dyer conjecture base change potential modularity

Citation

Virdol, Cristian. Base change and the Birch and Swinnerton-Dyer conjecture. Funct. Approx. Comment. Math. 46 (2012), no. 2, 189--194. doi:10.7169/facm/2012.46.2.4. https://projecteuclid.org/euclid.facm/1340628401


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References

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