
10. Geometric Extension Algebra

1. Problem 10.1.

[Peter McNamara] Given an algebraic group $G$ acting on a variety $X$ with finitely many orbits and a $G$-equivariant morphism $\pi\colon \widetilde{X} \to X$ where $\widetilde{X}$ is nonsingular (not necessarily connected), consider $A = \operatorname{End}^\bullet_{D^\mathrm{b}_G(X)}(\pi_* \underline{k}_{\widetilde{X}})$, an algebra over $H^G(pt, k)$. What geometric condition on $\pi$ is equivalent to $A$ being quasi-hereditary over $H^G(pt, k)$?

Cite this as: AimPL: Sheaves and modular representations of reductive groups, available at http://aimpl.org/sheavemodular.