In this lecture I will review geometric class field theory from the modern point of view of the Langlands program for GL_1. Starting from a rank one local system on a smooth projective curve over an algebraically closed field I will explain how to construct an equivariant rank one local system on the associated Picard scheme. This lecture is preparatory for the analog construction that will follow from the point of view of my geometrization conjecture for the local Langlands correspondence.

Laurent Fargues is Directeur de Recherche at CNRS / Institut de mathe ́matiques de Jussieu. He is a leading expert in questions on the local Langlands correspondence, Rapoport-Zink spaces, and p-adic Hodge theory, and has made striking contributions to all of these areas. His work is characterized by a unique vision of how these subjects are related, and his insights are shaping these fields. He received the "Petit d’Ormoy, Carrière, Thébault", prize given by the French Academy of Science. He is an invited sessional speaker at the upcoming 2018 ICM at Rio de Janeiro, Brazil.