Overconvergent de Rham-Witt cohomology

Abstract

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 WyX=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 Wy( OX) of Overconvergent Witt-vectors. If X is affine one proves that there is a 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.