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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