Perverse sheaves on semiabelian varieties

Abstract

We give a Tannakian description for the category of perverse sheaves on semiabelian varieties. Our construction is based on a vanishing theorem for the hypercohomology of perverse sheaves and extends earlier results for tori and abelian varieties. As an application we explain how perverse sheaves on abelian varieties can be studied in terms of semiabelian degenerations via a Tannakian interpretation for the functor of nearby cycles.