Koszul duality and semisimplicity of Frobenius

Pramod N. Achar (1) , Simon Riche (2)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Domaines: Théorie des représentations [math.RT]

Pramod N. Achar, Simon Riche. Koszul duality and semisimplicity of Frobenius. Annales de l'Institut Fourier, 2013, 63, pp.1511-1612. ⟨hal-00565745⟩