Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Applications of (higher) categorical trace II: Deligne-Lusztig theory

D. Gaitsgory, N. Rozenblyum, Y. Varshavsky

Abstract

We use the formalism of the (2-category) AGCat, developed in [GRV], and the operation of higher categorical trace to (re)derive a number of results in the Deligne-Lusztig theory.

Applications of (higher) categorical trace II: Deligne-Lusztig theory

Abstract

We use the formalism of the (2-category) AGCat, developed in [GRV], and the operation of higher categorical trace to (re)derive a number of results in the Deligne-Lusztig theory.

Paper Structure

This paper contains 120 sections, 122 theorems, 1147 equations.

Table of Contents

  1. What is this paper about?
  2. Categorical representations: general theory
  3. Categorical representations: the spectrally finite subcategory
  4. Independence of Deligne-Lusztig characters of the parabolic
  5. What else is done in this paper?
  6. Monodromicity and restricted categorical representations
  7. Example
  8. The hidden motivation for writing this paper
  9. Structure of the paper
  10. Conventions and notation
  11. Category theory
  12. An identity crisis
  13. Higher algebra
  14. Algebraic geometry
  15. Groups
  16. ...and 105 more sections

Key Result

Lemma 1.2.3

An object e:obj of arr is dualizable if and only if ${\mathbf{o}}_1,{\mathbf{o}}_2$ are dualizable as objects of ${\mathbf{O}}^{1\operatorname{-Cat}}$ and $t$ is adjointable. Moreover, in this case, the dual of e:obj of arr is given by

Theorems & Definitions (197)

  • Remark 3.4
  • Remark 3.6
  • Remark 4.2
  • Lemma 1.2.3
  • proof
  • Remark 1.3.3
  • Lemma 1.3.5
  • Remark 1.3.6
  • proof : Proof of Lemma \ref{['l:Trace dualizable']}
  • Theorem 1.3.8: BN1
  • ...and 187 more