Morse decomposition for D-module categories on stacks

Author: 

McGerty, K
Nevins, T

Publication Date: 

1 January 2017

Last Updated: 

2020-02-02T04:59:18.16+00:00

abstract: 

Let Y be a smooth algebraic stack exhausted by quotient stacks. Given a Kirwan-Ness stratification of the cotangent stack T^*Y, we establish a recollement package for twisted D-modules on Y, gluing the category from subquotients described via modules microsupported on the Kirwan-Ness strata of T^*Y. The package includes unusual existence and "preservation-of-finiteness" properties for functors of the full category of twisted D-modules, extending the standard functorialities for holonomic modules. In the case that Y = X/G is a quotient stack, our results provide a higher categorical analogue of the Atiyah-Bott--Kirwan--Ness "equivariant perfection of Morse theory" for the norm-squared of a real moment map. As a consequence, we deduce a modified form of Kirwan surjectivity for the cohomology of hyperkaehler/algebraic symplectic quotients of cotangent bundles.

Symplectic id: 

456239

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article