2014/02/28 by Kevin McGerty, McGerty, Kevin, Thomas Nevins +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AG #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1402.7365
preliminary version; comments welcome
arxiv created 2014/02/28 · openalex publication_date 2014/02/28 · arxiv updated 2014/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.