Koszul duality and semisimplicity of Frobenius

Details Koszul duality and semisimplicity of Frobenius Koszul duality and semisimplicity of Frobenius

2011-02-14

arxiv.org/abs/1102.2820v1

Mathematics

Representation Theory

76 pages

Scientific paper

A fundamental result of Beilinson-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 analogue. In particular, we show that these functors preserve semisimplicity of the Frobenius action.

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