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

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.

2 minor mistakes corrected

References in corpus (4)

• Higher Topos Theory
• The Harder-Narasimhan stratification of the moduli stack of G-bundles via Drinfeld's compactifications
• On some finiteness questions for algebraic stacks
• Bounds for Behrend's conjecture on the canonical reduction

Cited by in corpus (9)

• Topological Fukaya category and mirror symmetry for punctured surfaces
• The Atiyah-Bott formula for the cohomology of the moduli space of bundles on a curve
• On an invariant bilinear form on the space of automorphic forms via asymptotics
• The Harder-Narasimhan stratification of the moduli stack of G-bundles via Drinfeld's compactifications
• Remarks on Theta-stratifications and derived categories
• Geometric Bernstein Asymptotics and the Drinfeld-Lafforgue-Vinberg degeneration for arbitrary reductive groups
• Semi-infinite cohomology and Kazhdan-Lusztig equivalence at positive level
• Contractibility of the space of rational maps
• Functors given by kernels, adjunctions and duality