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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.