Overconvergent de Rham-Witt cohomology

TY - JOUR

T1 - Overconvergent de Rham-Witt cohomology

AU - Davis, Christopher James

AU - Langer, Andreas

AU - Zink, Thomas

PY - 2011

Y1 - 2011

N2 - 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 WtΩX/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 Wt (OX) 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.

AB - 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 WtΩX/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 Wt (OX) 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.

M3 - Journal article

SN - 0012-9593

VL - 44

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

IS - 2

ER -