Categorical cyclic homology and filtered D-modules on stacks: Koszul duality

2023/01/17 by Chen, Harrison
#14F08 #18M70 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2301.06949

Abstract

Motivated by applications to the categorical and geometric local Langlands correspondences, we establish an equivalence between the category of filtered D-modules on a smooth stack X and the category of S¹-equivariant ind-coherent sheaves on its formal loop space \widehatL X, exchanging compact D-modules with coherent sheaves, and coherent D-modules with continuous ind-coherent sheaves. The equivalence yields a sheaf of categories over \mathbbA¹/\mathbbG_m whose special fiber is a category of coherent sheaves on stacks appearing in categorical traces, and whose generic fiber is a category of equivariant constructible sheaves.

Related

• Derived category of equivariant coherent sheaves on a smooth toric variety and Koszul duality
• Ind-coherent sheaves
• Loop Spaces and Langlands Parameters
• Koszul Algebras and Sheaves over Projective Space
• Coherent sheaves, sheared D-modules, and Hochschild cochains