Module categories over affine supergroup schemes

Let k be an algebraically closed field of characteristic 0 or p>2. Let G be an affine supergroup scheme over k. We classify the indecomposable exact module categories over the tensor category sCohf(G) of (coherent sheaves of) finite dimensional O(G)-supermodules in terms of (H,Ψ)-equivariant coherent sheaves on G. We deduce from it the classification of indecomposable geometrical module categories over sRep(G). When G is finite, this yields the classification of all indecomposable exact module categories over the finite tensor category sRep(G). In particular, we obtain a classification of twists for the supergroup algebra kG of a finite supergroup scheme G, and then combine it with [7, Corollary 4.1] to classify finite dimensional triangular Hopf algebras with the Chevalley property over k.