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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Categorical cell decomposition of quantized symplectic algebraic varieties

Gwyn Bellamy, Christopher Dodd, Kevin McGerty and Thomas Nevins

Geometry & Topology 21 (2017) 2601–2681
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.

Keywords
quantization, symplectic, elliptic
Mathematical Subject Classification 2010
Primary: 53D55
Secondary: 14F05
References
Publication
Received: 7 May 2015
Revised: 23 May 2016
Accepted: 10 August 2016
Published: 15 August 2017
Proposed: Richard Thomas
Seconded: Dan Abramovich, Frances Kirwan
Authors
Gwyn Bellamy
School of Mathematics and Statistics
University of Glasgow
15 University Gardens
Glasgow
G12 8QW
United Kingdom
Christopher Dodd
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green Street
MC-382
Urbana, IL 61801
United States
Kevin McGerty
Mathematical Institute
University of Oxford
Andrew Wiles Building
Woodstock Road
Oxford
OX2 6GG
United Kingdom
Thomas Nevins
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green Street
MC-382
Urbana, IL 61801
United States