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Koszul duality and semisimplicity of Frobenius

Pramod N. Achar, Simon Riche (2013)

Annales de l’institut Fourier

A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of ℓ -adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated...

Koszul duality for N-Koszul algebras

Roberto Martínez-Villa, Manuel Saorín (2005)

Colloquium Mathematicae

The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of A ∞ algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.

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