Program
Loo-Keng Hua Distinguished Lecture
Student No.:100
Time:16:30-17:30, Apr.3,9,10,12
Instructor:Laurent Fargues  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-4-3
Ending Date:2018-4-13

 

*3rd Lecture changed to Apr.10 (Tue)

 

1st Lecture: Classical geometric class field theory

Time: Tue 16:30-17:30, Apr.3

 

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.

 


2nd Lecture: The fundamental curve of p-adic Hodge theory

Time: Mon 16:30-17:30, Apr.9

 

I will review the construction and the structure of the fundamental curve of p-adic Hodge theory introduced and studied in my joint work with Jean-Marc Fontaine. This curve has different flavors and can either be considered as the analog of a projective smooth algebraic curve (a Dedekind scheme over the p-adic numbers but not of finite type) or the analog of a compact Riemann surface (a quasicompact partially proper adic space over the p-adic numbers that is not topologically of finite type). In the meantime I will explain some elementary structure results for "holomorphic functions of the variable p".

 


3rd Lecture: Structure of the Picard stack of line bundles on the curve and of the Hilbert diamond of positive divisors on the curve

Time: Tue 16:30-17:30, Apr.10

 

In this lecture I will speak about the fundamental curve "in family". Here the family is parametrized by a characteristic p perfectoid space.

I will explain the structure of the Picard stack of line bundles in this context. Moreover I will explain the structure of positive degree effective divisors on the curve as a diamond in the sens of Scholze.

 


4th Lecture: Structure of the Abel-Jacobi morphism and local class field theory

Time: Thu 16:30-17:30, Apr.12

 

In this final lecture I will explain that in high degree the Abel-Jacobi morphism in my context is a pro-étale locally trivial fibration in simply connected diamonds. As a corollary I deduce my geometrization conjecture for GL_1. I will explain how this is linked to the classical local class field theory.

 

 

 

Bio: 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.