Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(5): 1803-1825

Online first article September 13, 2017      Printed September 30, 2017

https://doi.org/10.4134/BKMS.b160758

Copyright © The Korean Mathematical Society.

Equivariant matrix factorizations and Hamiltonian reduction

Sergey Arkhipov, Tina Kanstrup

Aarhus Universitet, Hausdorff Center for Mathematics

Abstract

Let $X$ be a smooth scheme with an action of an algebraic group $G$. We establish an equivalence of two categories related to the corresponding moment map $\mu : T^*X \to \g^*$ - the derived category of $G$-equivariant coherent sheaves on the derived fiber $\mu^{-1}(0)$ and the derived category of $G$-equivariant matrix factorizations on $T^*X \times \g$ with potential given by $\mu$.

Keywords: DG-modules, equivariant sheaves, Hamiltonian reduction, matrix factorizations

MSC numbers: 16G99, 14F05, 14F43

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