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10. Geometric Extension Algebra


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      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.