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

1 Citation (Scopus)

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 Jan 1

Fingerprint

All Science Journal Classification (ASJC) codes

Mathematics(all)

Cite this

Virdol, C. (2012). Base change and the birch and swinnerton-dyer conjecture. Functiones et Approximatio, Commentarii Mathematici, 46(2), 189-194. https://doi.org/10.7169/facm/2012.46.2.4

@article{96d7e5c5933a4bf780ca2772edf1dfdb,

title = "Base change and the birch and swinnerton-dyer conjecture",

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",

year = "2012",

month = jan

day = "1",

doi = "10.7169/facm/2012.46.2.4",

language = "English",

volume = "46",

pages = "189--194",

journal = "Functiones et Approximatio, Commentarii Mathematici",

issn = "0208-6573",

publisher = "Adam Mickiewicz University Press",

number = "2",

}

TY - JOUR

T1 - Base change and the birch and swinnerton-dyer conjecture

AU - Virdol, Cristian

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84983535087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983535087&partnerID=8YFLogxK

U2 - 10.7169/facm/2012.46.2.4

DO - 10.7169/facm/2012.46.2.4

M3 - Article

AN - SCOPUS:84983535087

VL - 46

SP - 189

EP - 194

JO - Functiones et Approximatio, Commentarii Mathematici

JF - Functiones et Approximatio, Commentarii Mathematici

SN - 0208-6573

IS - 2

ER -

Access to Document

10.7169/facm/2012.46.2.4