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Abstract:
Hasse and Weil conjectured that Zeta functions of varieties over number
fields admit meromorphic continuation and satisfy a functional equation.
We will explain new results in the direction of this conjecture for genus
2 curves over totally real fields. The difficulty is that genus 2 curves
have non-regular hodge numbers and the Taylor--Wiles method that was
successful in proving the conjecture for genus 1 curves (for example)
breaks down in several places. This is joint work with G. Boxer, F.
Calegari and T. Gee.
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