Compact generation of the category of D-modules on the stack of G-bundles on a curve

TL;DR

This paper proves that the derived category of D-modules on the stack of G-bundles over a curve is compactly generated by expressing the stack as a union of manageable open substacks.

Contribution

It demonstrates the compact generation of D-modules on Bun_G(X) despite its non-quasi-compactness, using a union of co-truncative open substacks approach.

Findings

The category of D-modules on Bun_G(X) is compactly generated.

Bun_G(X) can be expressed as a union of quasi-compact co-truncative substacks.

The approach facilitates further analysis of D-modules on algebraic stacks.

Abstract

The goal of the paper is to show that the (derived) category of D-modules on the stack Bun_G(X) is compactly generated. Here X is a smooth complete curve, and G is a reductive group. The problem is that Bun_G(X) is not quasi-compact, so the above compact generation is not automatic. The proof is based on the following observation: Bun_G(X) can be written as a union of quasi-compact open substacks, which are "co-truncative", i.e., the j_! extension functor is defined on the entire category of D-modules.