On the middle convolution

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.