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)

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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, Dr 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

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