Equivariant Matrix Factorizations and Hamiltonian reduction

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 $\mu :T^{\ast }X\to Lie(G{)}^{\ast }$ - 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 $T^{\ast }X\times Lie(G)$ with potential given by $\mu$.

22 pages