Ind-coherent sheaves

TL;DR

This paper develops the theory of ind-coherent sheaves on schemes and stacks, highlighting their differences from quasi-coherent sheaves and their importance in the categorical Geometric Langlands Correspondence.

Contribution

It introduces the theory of ind-coherent sheaves, clarifying their properties and role in advanced geometric and categorical frameworks.

Findings

Ind-coherent sheaves are closely related but distinct from quasi-coherent sheaves.

The difference between these categories is crucial for the categorical Geometric Langlands Correspondence.

The paper provides foundational tools for future research in geometric representation theory.

Abstract

We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial for the formulation of the categorical Geometric Langlands Correspondence.