Equivariant matrix factorizations and Hamiltonian reduction
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초록
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 $\mu$.
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 $\mu$.
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