School of Mathematics Colloquium

On the Hasse-Weil conjecture.

by Prof. Vincent Pilloni (Ecole normale superieure de Lyon, France)

Thursday, February 28, 2019 from to (Asia/Kolkata)
at AG-69
Description
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.