Support varieties and representation types for basic classical Lie superalgebras

Let κ be an algebraically closed field of characteristic p>3 and g a restricted Lie superalgebra over κ. We introduce the definition of restricted cohomology for g and show its cohomology ring is finitely generated provided g is a basic classical Lie superalgebra. As a consequence, we show that the restricted enveloping algebra of a basic classical Lie superalgebra g is always wild except g=sl2 or g=osp(1|2) or g=C(2).