Base change and the birch and swinnerton-dyer conjecture

Cristian Virdol

doi:10.7169/facm/2012.46.2.4

Base change and the birch and swinnerton-dyer conjecture

Cristian Virdol

Department of Mathematics

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

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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.

Original language	English
Pages (from-to)	189-194
Number of pages	6
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	46
Issue number	2
DOIs	https://doi.org/10.7169/facm/2012.46.2.4
Publication status	Published - 2012

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.7169/facm/2012.46.2.4

Cite this

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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.",

author = "Cristian Virdol",

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doi = "10.7169/facm/2012.46.2.4",

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AB - 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.

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ER -

Base change and the birch and swinnerton-dyer conjecture

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