Rights accessRestricted access - publisher's policy
The main result of this paper is a characterization of the abelian varieties B=K defined over
Galois number fields with the property that the L-function L(B=K; s) is a product of L-functions of
non-CM newforms over Q for congruence subgroups of the form T1(N). The characterization involves
the structure of End(B), isogenies between the Galois conjugates of B, and a Galois cohomology
class attached to B=K.
We call the varieties having this property strongly modular. The last section is devoted to the study
of a family of abelian surfaces with quaternionic multiplication. As an illustration of the ways in which
the general results of the paper can be applied, we prove the strong modularity of some particular
abelian surfaces belonging to that family, and we show how to find nontrivial examples of strongly
modular varieties by twisting.
CitationGuitart, X.; Quer, J. Modular abelian varieties over number fields. "Canadian journal of mathematics. Journal canadien de mathématiques", 2014, vol. 66, núm. 1, p. 170-196.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: firstname.lastname@example.org