#### Volume 21, issue 5 (2017)

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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 $\mathsc{D}$–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 ${\mathbb{G}}_{m}$. 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
Primary: 53D55
Secondary: 14F05