Modular abelian varieties over number fields

Details Modular abelian varieties over number fields Modular abelian varieties over number fields

2009-05-15

arxiv.org/abs/0905.2550v1

Mathematics

Number Theory

24 pages

Scientific paper

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 zeta function $L(B/K;s)$ is equivalent to the product of zeta functions of non-CM newforms for congruence subgroups $\Gamma_1(N)$. 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, we show how to find nontrivial examples of strongly modular varieties by twisting, and prove the existence of strongly modular surfaces satisfying certain properties.

Affiliated with

Also associated with

No associations

Rating

Modular abelian varieties over number fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Modular abelian varieties over number fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modular abelian varieties over number fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-524476