Module categories over affine supergroup schemes

Abstract

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 sCoh f ( 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 k G 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 .