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 $D_G^b(X;{\overline{\mathbb{Q}}}_{\ell })\simeq D_G^b(\mathbf{Perv}(X;{\overline{\mathbb{Q}}}_{\ell }))$ 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.

40 Pages. Comments welcome!