Modularity of abelian surfaces with Quaternionic Multiplication

Details Modularity of abelian surfaces with Quaternionic Multiplication Modularity of abelian surfaces with Quaternionic Multiplication

2003-04-27

arxiv.org/abs/math/0304431v1

Mathematics

Number Theory

to appear at Math. Res. Letters

Scientific paper

We prove that any abelian surface defined over $\Q$ 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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