April 26, 14h -- Altan Erdnigor
The Artin's reciprocity law for a function field k(X) for a curve X over a finite field k can be interpreted as an isomorphism between the profinite completion of the Picard group and the abelianization of the étale fundamental group. I will explain the Deligne's proof of the Artin's reciprocity law in the unramified case via an equivalence of categories of l-adic local systems of rank one on X and Picard variety Pic(X) with some compatibilities by taking the pullback of the Abel-Jacobi map. Time permitting, we will discuss ramified, local, and characteristic zero versions of geometric class field theory.