Overconvergent de Rham-Witt cohomology
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 44 (2011) no. 2, p. 197-262

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 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.

Le but de ce travail est de construire, pour X une variété lisse sur un corps parfait k de caractéristique finie, un complexe de de Rham-Witt surconvergent W Ω X/k comme un sous-complexe convenable du complexe de de Rham-Witt de Deligne-Illusie. Ce complexe qui est fonctoriel en X est un complexe de faisceaux étales et une algèbre différentielle graduée sur l’anneau W (𝒪 X ) des vecteurs de Witt surconvergents. Lorsque X est affine, on démontre qu’il existe un isomorphisme canonique entre la cohomologie de Monsky-Washnitzer et la cohomologie (rationnelle) de de Rham-Witt surconvergente. Finalement on définit pour X quasi-projectif un isomorphisme entre la cohomologie rigide de X et la cohomologie de de Rham-Witt surconvergente rationnelle.

DOI : https://doi.org/10.24033/asens.2143
Classification:  14F30,  14F40
Keywords: rigid cohomology, de Rham-Witt complex
@article{ASENS_2011_4_44_2_197_0,
     author = {Davis, Christopher and Langer, Andreas and Zink, Thomas},
     title = {Overconvergent de Rham-Witt cohomology},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 44},
     number = {2},
     year = {2011},
     pages = {197-262},
     doi = {10.24033/asens.2143},
     zbl = {1236.14025},
     mrnumber = {2830387},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2011_4_44_2_197_0}
}
Davis, Christopher; Langer, Andreas; Zink, Thomas. Overconvergent de Rham-Witt cohomology. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 44 (2011) no. 2, pp. 197-262. doi : 10.24033/asens.2143. http://www.numdam.org/item/ASENS_2011_4_44_2_197_0/

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