  Let $mathfrak{g}$ be a restricted Lie superalgebra over an algebraically
closed field $k$ of characteristic $p>2$. Let $\mathfrak{u}(\mathfrak{g})$
denote the restricted enveloping algebra of $\mathfrak{g}$. In this paper we
prove that the cohomology ring $\HH^\bullet(\fu(\fg), k)$ is finitely
generated. This allows one to define support varieties for finite dimensional
$\fu(\fg)$-supermodules. We also show that support varieties for finite
dimensional $\fu(\fg)$ supermodules satisfy the desirable properties of support
variety theory.
