Resumen de Support varieties for transporter category algebras

Fei Xu

• Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the G-space BP, while the k-category algebra of the transporter category is the (Gorenstein) skew group algebra on the G-algebra kP.

  We introduce a support variety theory for the category algebras of transporter categories.

  It extends Carlson�s support variety theory on group cohomology rings to equivariant cohomology rings. In the mean time it provides a class of (usually non selfinjective) algebras to which Snashall�Solberg�s (Hochschild) support variety theory applies. Various properties will be developed. Particularly we establish a Quillen stratification for modules.