2011/02/14 by Pramod N. Achar, Achar, Pramod N., Simon Riche +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1102.2820
76 pages
arxiv created 2011/02/14 · arxiv updated 2011/02/15
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.