Categorical cell decomposition of quantized symplectic algebraic varieties

Bellamy, G. , Dodd, C., McGerty, K. and Nevins, T. (2017) Categorical cell decomposition of quantized symplectic algebraic varieties. Geometry and Topology, 21(5), pp. 2601-2681. (doi: 10.2140/gt.2017.21.2601)

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 BiałynickiBirula 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bellamy, Professor Gwyn
• Authors: Bellamy, G., Dodd, C., McGerty, K., and Nevins, T.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Geometry and Topology
• Publisher: Mathematical Sciences Publishers
• ISSN: 1465-3060
• ISSN (Online): 1364-0380
• Copyright Holders: Copyright © 2017 Mathematical Sciences Publishers
• First Published: First published in Geometry and Topology 21(5):2601-2681
• Publisher Policy: Reproduced with the permission of the publisher