Mathematical Research Letters

Volume 10 (2003)

Number 2

Modularity of Abelian Surfaces with Quaternionic Multiplication

Pages: 145 – 150

DOI: http://dx.doi.org/10.4310/MRL.2003.v10.n2.a1

Author

Luis Dieulefait (Université de Paris 13)

Abstract

We prove that any abelian surface defined over $\mathbb Q$ of $GL_2$-type having quaternionic multiplication and good reduction at $3$ is modular. We generalize the result to higher dimensional abelian varieties with “sufficiently many endomorphisms.”

Full Text (PDF format)