Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Local systems with restricted variation on the formal punctured disc via factorization

Ekaterina Bogdanova

Abstract

We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over $\operatorname{Rep}(G)$. Along the way we develop a theory of factorization structures in families and study functorialities of such under changes of the base curve.

Local systems with restricted variation on the formal punctured disc via factorization

Abstract

We define the stack of -local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over . Along the way we develop a theory of factorization structures in families and study functorialities of such under changes of the base curve.

Paper Structure

This paper contains 58 sections, 80 theorems, 389 equations.

Table of Contents

  1. Introduction
  2. Local geometric Langlands
  3. A sibling: restricted local geometric Langlands.
  4. Statement of the result
  5. From local systems on the punctured disc to factorization modules over $\mathop{\mathrm{Rep}}\nolimits(\check{G})$.
  6. The stack of local systems with restricted variation on the puntured disc.
  7. Main result.
  8. Motivation
  9. Outline of the argument
  10. Notation and conventions
  11. Lie theory.
  12. Higher categories.
  13. Higher algebra.
  14. DG categories.
  15. Derived algebraic geometry.
  16. ...and 43 more sections

Key Result

Theorem 1.2

There exists a fully faithful functor that preserves the forgetful functors from both sides to $\mathbf{DGCat}$. Here

Theorems & Definitions (211)

  • Conjecture 1
  • Theorem 1.2
  • Theorem 1.4
  • Corollary 1.4.1
  • Definition 2.1.2
  • Remark 2.1.3
  • Definition 2.1.4: CF
  • Definition 2.1.5: CF
  • Definition 2.1.10: CF
  • Remark 2.1.11
  • ...and 201 more