A fundamental result of Beǐlinson-Ginzburg-Soergel states that on flag varieties and related spaces, a certain modified version of the category of 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. © Association des Annales de l'institut Fourier, 2013.
Publication Source (Journal or Book title)
Annales de l'Institut Fourier
Achar, P., & Riche, S. (2013). Koszul duality and semisimplicity of frobenius. Annales de l'Institut Fourier, 63 (4), 1511-1612. https://doi.org/10.5802/aif.2809