  Let R be a regular, local and F-finite ring defined over a field of finite
characteristic. Let I be an ideal of height c with normal quotient $A=R/I$. It
is shown that the local cohomology module H^c_I(R) contains a unique simple
D_R--submodule L(A,R). This should be viewed as a finite characteristic analog
of the Kashiwara--Brylinski D_R--module in characteristic zero which
corresponds to the intersection cohomology complex via the Riemann--Hilbert
correspondence. Besides the existence of L(A,R), more importantly, we give its
construction as a certain dual of the tight closure of zero in $H^d_m(A)$. We
obtain a precise D_R--simplicity criterion for H^c_I(R), namely H^c_I(R) is
D_R--simple if and only if the tight closure of zero in H^d_m(A) is Frobenius
nilpotent, in particular this is the case if A is F--rational.
  Furthermore, the techniques developed imply a result in tight closure theory,
saying that the parameter test module commutes with completion.
