Mer continuation and functional equations of Abelian curves over totally real fields

Abelian Surfaces over totally real fields are Potentially Modular

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular.We furthermore show the modularity of infinitely many abeliansurfaces over q with end_c(a)=z.We also deduce modularity and potential modularity results for genus one curves over (not necessarily cm) quadraticextensions of totally real fields.