Papers › Abelian Surfaces over totally real fields are Potentially Modular
Abelian Surfaces over totally real fields are Potentially Modular
George Boxer, Frank Calegari, Toby Gee, Vincent Pilloni
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We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse--Weil zeta functions. We furthermore show the modularity of infinitely many abelian surfaces A over Q with End_C(A)=Z. We also deduce modularity and potential modularity results for genus one curves over (not necessarily CM) quadratic extensions of totally real fields.
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