Modularity of abelian surfaces with Quaternionic Multiplication

Abstract

We prove that any abelian surface defined over $\Q$ of $G{L}_2$-type having quaternionic multiplication and good reduction at 3 is modular. We generalize the result to higher dimensional abelian varieties with ``sufficiently many endomorphisms".

to appear at Math. Res. Letters

References in corpus (1)

• The arithmetic of QM-abelian surfaces through their Galois representations