  For any power $q$ of the positive ground field characteristic, a smooth
$q$-bic threefold -- the Fermat threefold of degree $q+1$ for example -- has a
smooth surface $S$ of lines which behaves like the Fano surface of a smooth
cubic threefold. I develop projective, moduli-theoretic, and degeneration
techniques to study the geometry of $S$. Using, in addition, the modular
representation theory of the finite unitary group and the geometric theory of
filtrations, I compute cohomology of the structure sheaf of $S$ when $q$ is
prime.
