Categorical cell decomposition of quantized symplectic algebraic varieties

Gwyn Bellamy, Christopher Dodd, Kevin McGerty, Thomas Nevins

Research output: Contribution to journalArticlepeer-review

Abstract

We prove a new symplectic analogue of Kashiwara’s equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation-quantizations that mirrors, at a higher categorical level, the Białynicki-Birula stratification of a variety with an action of the multiplicative group Gm. The resulting categorical cell decomposition provides an algebrogeometric parallel to the structure of Fukaya categories of Weinstein manifolds. From it, we derive concrete consequences for invariants such as K-theory and Hochschild homology of module categories of interest in geometric representation theory.

Original languageEnglish (US)
Pages (from-to)2601-2681
Number of pages81
JournalGeometry and Topology
Volume21
Issue number5
DOIs
StatePublished - Aug 15 2017

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint Dive into the research topics of 'Categorical cell decomposition of quantized symplectic algebraic varieties'. Together they form a unique fingerprint.

Cite this