Vincent Pilloni
Ecole normale superieure de Lyon, France
February 28, 2019
On the Hasse-Weil conjecture: Hasse and Weil conjectured that Zeta functions of varieties over numberfields 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.
Ecole normale superieure de Lyon, France
February 28, 2019
On the Hasse-Weil conjecture: Hasse and Weil conjectured that Zeta functions of varieties over numberfields 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.