  We give a description of certain local cohomology invariants (introduced by
Lyubeznik) for a class of mildly singular varieties in positive characteristic.
The novelty of our approuch lies in using the new Riemann-Hilbert type
correspondenc of Emerton and Kisin to express these invariants in terms of
'etale cohomology with ZZ/pZZ coefficients. Thus we are able to obtain results
in positive characteristic whereas earlier approaches were restricted (due to
the use of de Rham theory) to the analytic case.
