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

Cristian Virdol

doi:10.1016/j.jnt.2010.11.008

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

Cristian Virdol

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	681-684
Number of pages	4
Journal	Journal of Number Theory
Volume	131
Issue number	4
DOIs	https://doi.org/10.1016/j.jnt.2010.11.008
Publication status	Published - 2011 Apr

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2010.11.008

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

author = "Cristian Virdol",

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

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

Abstract

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