On some finiteness questions for algebraic stacks

Abstract

We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG category of quasi-coherent sheaves is continuous.

References in corpus (2)

• Higher Topos Theory
• Singular support of coherent sheaves, and the geometric Langlands conjecture

Cited by in corpus (7)

• Loop group actions on categories and Whittaker invariants
• Compact generation of the category of D-modules on the stack of G-bundles on a curve
• Singular support of coherent sheaves, and the geometric Langlands conjecture
• Symmetries of categorical representations and the quantum Ngô action
• On a strange invariant bilinear form on the space of automorphic forms
• Contractibility of the space of rational maps
• Functors given by kernels, adjunctions and duality