Equivariant matrix factorizations and Hamiltonian reduction
Bull. Korean Math. Soc. 2017 Vol. 54, No. 5, 1803-1825
Published online September 13, 2017
Printed September 30, 2017
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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