Mathematical Research Letters

Volume 10, Issue 2, March 2003 pp. 145-150.

Modularity of Abelian Surfaces with Quaternionic Multiplication

Authors: Luis Dieulefait
Author institution: Université de Paris 13

Summary: 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."

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