  We present a cohomological interpretation of the middle convolution functor
MC and find an explicit Riemann-Hilbert correspondence for MC_\lambda. This
leads to an algorithm for the construction of Fuchsian systems which correspond
to irreducible rigid local systems under the Riemann-Hilbert correspondence.
Also, the effect of MC_\lambda on the p-curvatures ist determined and new
examples of differential systems are found which satisfy the Grothendieck-Katz
p-curvature conjecture.
