A Langlands stack (under construction)


Updated Nov.12,2014: A new version of Arinkin-Gaitsgory on reformulation of the GLC

Leisure readings
Vergne  All what I wanted to know about Langlands program and was afraid to ask
Gelbart  An elementary introduction to the Langlands program
Frenkel  Recent Advances in the Langlands Program

I.Papers & Books

0.Tools
Gaitsgory  Geometric representation theory
Kac   Infinite dimensional Lie algebras
Frenkel, Ben-Zvi  Vertex algebras and algebraic curves
Beilinson, Drinfel’d   Chiral algebras
Arthur  An introduction to the trace formula

1.Langlands Program for number fields
1.1 Local Langlands for \Bbb C and \Bbb R

1.2 Local Langlands for p-adic fields
Harris, Taylor  The geometry and cohomology of some simple Shimura varieties
Henniart  Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

1.3 Fundamental Lemma
Waldspurger  Endoscopie et changement de caractéristique
Ngô  Fibration de Hitchin et endoscopie
Laumon, Ngô  Le lemme fondamental pour les groupes unitaires
Waldspurger  L’endoscopie tordue n’est pas si tordue
Ngô  Le lemme fondamental pour les algèbres de Lie

2.Langlands Program for function fields
Drinfel’d  Elliptic modules I,II
Laumon  Cohomology of Drinfeld modular varieties I,II
Lafforgue  Chtoucas de Drinfeld et applications
Lafforgue  Chtoucas de Drinfeld, formule des traces d’Arthur-Selberg et correspondance de Langlands

3.Geometric Langlands Program
Arinkin, Gaitsgory  Singular support of coherent sheaves, and the geometric Langlands conjecture
Witten  Quantum field theory, Grassmannians and algebraic curves
Kapustin, Witten  Electric-Magnetic Duality And The Geometric Langlands Program
Frenkel, Gaitsgory, Vilonen  On the geometric Langlands conjecture
Frenkel  Lectures on the Langlands Program and Conformal Field Theory
Donagi, Pantev  Lectures on the geometric Langlands conjecture and non-abelian Hodge theory

II.On-line Resources
The Work of Robert Langlands: the official on-line archive for Robert Langlands’ work
Northwestern Geometric Langlands Program maintained by Vilonen, Frenkel, Gaitsgory and Goresky
Chicago Geometric Langlands Seminar
Note by Dennis Gaitsgory
Homepage of Edward Frenkel
GRASP run by David Ben-Zvi

4 thoughts on “A Langlands stack (under construction)

  1. hyh says:

    Frenkel 还推荐过 Gelbart 写的 An Elementary Introduction to Langlands Program 。1984年写的,他现在还推荐。

    给你个链接吧:https://www.dropbox.com/sh/tbxuynuxabrzw2z/dHJHFKEcvr/Math/Geomtric%20Langlands

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