### Base change and the Birch and Swinnerton-Dyer conjecture

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

#### 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.

First Page:
Primary Subjects: 11F41
Secondary Subjects: 11F80, 11R42, 11R80, 11G05
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Permanent link to this document: http://projecteuclid.org/euclid.facm/1340628401
Digital Object Identifier: doi:10.7169/facm/2012.46.2.4
Zentralblatt MATH identifier: 06074838
Mathematical Reviews number (MathSciNet): MR2931665

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