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Creators/Authors contains: "Pilloni, Vincent"

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  1. ; ; ; (, Publications mathématiques de l'IHÉS)
    Abstract 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  $$A$$ A over  $${\mathbf {Q}}$$ Q with  $$\operatorname{End}_{ {\mathbf {C}}}A={\mathbf {Z}}$$ 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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