Langlands correspondence and Bezrukavnikov's equivalence

2021/03/03 by Anna Romanov, Romanov, Anna, Geordie Williamson +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2103.02329

openalex publication_date 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical point of view. The second part gives enough background in geometric representation theory to understand Bezrukavnikov's equivalence, which is a categorification of Kazhdan and Lusztig's two realizations of the affine Hecke algebra.

Citations

• The notion of category over an algebraic stack

Related

• Geometrization of the local Langlands correspondence: an overview
• On the geometrization of the local Langlands correspondence
• The work of Robert Langlands
• Travaux de Frenkel, Gaitsgory et Vilonen sur la correspondance de Drinfeld-Langlands
• Recent Advances in the Langlands Program