# Derived categories of character sheaves

## TL;DR

This paper provides a block decomposition of the dg category of character sheaves on a complex reductive group, linking it to quasi-coherent sheaves on a derived stack, thus advancing the understanding of their categorical structure.

## Contribution

It introduces a block decomposition of the dg category of character sheaves and identifies it with quasi-coherent sheaves on an explicitly defined derived stack.

## Key findings

- Block decomposition of the dg category of character sheaves.
- Identification of character sheaves with quasi-coherent sheaves on a derived stack.
- Explicit description of the derived stack $\, ext{ extasciitilde}G$.

## Abstract

We give a block decomposition of the dg category of character sheaves on a simple and simply-connected complex reductive group $G$, similar to the one in generalized Springer correspondence. As a corollary, we identify the category of character sheaves on $G$ as the category of quasi-coherent sheaves on an explicitly defined derived stack $\widehat{G}$.