  We describe the support of $F$-finite $F$-modules over polynomial rings $R$
of prime characteristic. Our description yields an algorithm to compute the
support of such modules; the complexity of our algorithm is also analyzed. To
the best of our knowledge, this is the first algorithm to avoid extensive use
of Gr\"obner bases and hence of substantial practical value. We also use the
idea behind this algorithm to prove that the support of $H^j_I(S)$ is Zariski
closed for each ideal $I$ of $S$ where $R$ is noetherian commutative ring of
prime characteristic with finitely many isolated singular points and $S=R/gR$
($g\in R$).
