On the Equivariant Derived Category of Perverse Sheaves
Abstract: In this paper we extend Beilinson's realization formalism for triangulated categories and filtered triangulated categories to a pseudofunctorial and pseudonatural setting. As a consequence we prove an equivariant version of Beilinson's Theorem: for any algebraic group $G$ over an algebraically closed field $K$ and for any $G$-variety $X$, there is an equivalence of categories $D_Gb(X; \overline{\mathbb{Q}}{\ell}) \simeq D_Gb(\mathbf{Perv}(X;\overline{\mathbb{Q}}{\ell}))$ where $\ell$ is an integer prime coprime to the characteristic of $K$. We also show that the equivariant analogues of the other non-$D$-module aspects of Beilinson's Theorem hold in the equivariant case.
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