Overconvergent de Rham-Witt cohomology
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Overconvergent de Rham-Witt cohomology. / Davis, Christopher James; Langer, Andreas; Zink, Thomas.
I: Annales Scientifiques de l'Ecole Normale Superieure, Bind 44, Nr. 2, 2011.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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 as a suitable subcomplex 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 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 as a suitable subcomplex 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 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
VL - 44
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
SN - 0012-9593
IS - 2
ER -
ID: 64386596