Modularity of abelian surfaces with Quaternionic Multiplication

2003/04/27 by Luis Dieulefait, Dieulefait, Luis
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0304431

to appear at Math. Res. Letters

arxiv created 2003/04/27 · arxiv updated 2009/11/30

Abstract

We prove that any abelian surface defined over \Q of GL₂-type having quaternionic multiplication and good reduction at 3 is modular. We generalize the result to higher dimensional abelian varieties with ``sufficiently many endomorphisms".

Related

• Some modular abelian surfaces
• Modularity theorems for abelian surfaces
• Modularity theorems for abelian surfaces
• The arithmetic of QM-abelian surfaces through their Galois representations
• On abelian surfaces with potential quaternionic multiplication