PUB - Publikationen an der Universität Bielefeld

The goal of this work is to construct, for a smooth variety X over a perfect field k of finite characteristic p > 0, an overconvergent de Rham-Witt complex W(dagger)Omega(X/k) as a suitable sub-complex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in X, is a complex of etale sheaves and a differential graded algebra over the ring W(dagger)(O(X)) of overconvergent Witt-vectors. If X is Aline one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent de Rham-Witt cohomology. Finally we define for a quasiprojective X an isomorphism between the rational overconvergent de Rham-Witt cohomology and the rigid cohomology.