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Overconvergent de Rham-Witt cohomology

Christopher DavisAndreas LangerThomas Zink — 2011

Annales scientifiques de l'École Normale Supérieure

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 Ω X / k as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in X , is a complex of étale sheaves and a differential graded algebra over the ring W ( 𝒪 X ) of overconvergent Witt-vectors. If X is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

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