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Categorical cell
decomposition of quantized symplectic algebraic varieties
Gwyn Bellamy, Christopher Dodd, Kevin McGerty and Thomas Nevins |
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Geometry & Topology 21 (2017) 2601–2681
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Abstract |
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We prove a new symplectic analogue of Kashiwara’s equivalence from –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 . 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 –theory and Hochschild homology of module categories of interest in geometric representation theory. |
Keywords
quantization, symplectic, elliptic
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Mathematical Subject Classification 2010
Primary: 53D55
Secondary: 14F05
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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
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Authors |
| Gwyn Bellamy | |
| School of Mathematics and
Statistics University of Glasgow 15 University Gardens Glasgow G12 8QW United Kingdom |
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| Christopher Dodd | |
| Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green Street MC-382 Urbana, IL 61801 United States |
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| Kevin McGerty | |
| Mathematical Institute University of Oxford Andrew Wiles Building Woodstock Road Oxford OX2 6GG United Kingdom |
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| Thomas Nevins | |
| Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green Street MC-382 Urbana, IL 61801 United States |
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