| The classical Riemann-Hilbert correspondence gives a correspondence between linear systems of differential equations on a smooth analytic variety X and sheaves of local solutions to such a system. In the language of category theory this can be stated as an equivalence of categories between the category of coherent modules with integrable connection on X and the category of locally constant finite dimensional C-vector spaces on X. For smooth proper maps, this correspondence is functorial with respect to direct images. We give a proof of this compatibility and then extend it to the logarithmic setting as described by L. Illusie, K. Kato, and C. Nakayama and by A. Ogus. |
