Convolution groups of perverse sheaves on abelian varieties

Abelian varieties are projective varieties with a group structure. The group law induces a convolution operation for perverse sheaves, which are singular version of local systems. Via the Tannakian formalism, Krämer and Weissauer assign a linear group to each perverse sheaf. Given a family of perverse sheaves, we show that the convolution group of a very general perverse sheaf in the family is the same as the generic one. We give a geometric application to subvarieties of abelian varieties. This is joint work with Anna Cadoret.