2020/07/06 by Alessio Cipriani, Cipriani, Alessio, Jon Woolf +1
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2007.03060
Let X be a topologically stratified space, p be any perversity on X, and k be a field. We show that the category of p-perverse sheaves on X, constructible with respect to the stratification and with coefficients in k, is equivalent to the category of finite-dimensional modules over a finite-dimensional algebra if and only if X has finitely many strata and the same holds for the category of local systems on each of these. The main component in the proof is a construction of projective covers for simple perverse sheaves.