TY - JOUR
T1 - On the Birch and Swinnerton-Dyer conjecture for abelian varieties attached to Hilbert modular forms
AU - Virdol, Cristian
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/4
Y1 - 2011/4
N2 - 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.
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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U2 - 10.1016/j.jnt.2010.11.008
DO - 10.1016/j.jnt.2010.11.008
M3 - Article
AN - SCOPUS:78651062023
VL - 131
SP - 681
EP - 684
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 4
ER -