  We prove that the cohomology ring of a finite-dimensional restricted Lie
superalgebra over a field of characteristic $p > 2$ is a finitely-generated
algebra. Our proof makes essential use of the explicit projective resolution of
the trivial module constructed by J. Peter May for any graded restricted Lie
algebra. We then prove that the cohomological finite generation problem for
finite supergroup schemes over fields of odd characteristic reduces to the
existence of certain conjectured universal extension classes for the general
linear supergroup $GL(m|n)$ that are similar to the universal extension classes
for $GL_n$ exhibited by Friedlander and Suslin.
