Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex. / Davis, Christopher James; Zureick-Brown, David.
I: Mathematical Research Letters, Bind 21, Nr. 2, 2014, s. 281 – 288.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
AU - Davis, Christopher James
AU - Zureick-Brown, David
PY - 2014
Y1 - 2014
N2 - In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we prove that the integral Monsky-Washnitzer cohomology groups are well-defined, for any nonsingular affine variety over a perfect field of characteristic p. We then compare these cohomology groups with overconvergent de Rham-Witt cohomology. It was shown earlier that if the affine variety has small dimension relative to the characteristic of the ground field, then the cohomology groups are isomorphic. We extend this result to show that for any nonsingular affine variety, regardless of dimension, we have an isomorphism between integral Monsky-Washnitzer cohomology and overconvergent de Rham-Witt cohomology in degrees which are small relative to the characteristic.
AB - In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology groups. It seems to be well-known among experts that their construction always gives well-defined integral cohomology groups, but this fact also does not appear to be explicitly written down anywhere. In this paper, we prove that the integral Monsky-Washnitzer cohomology groups are well-defined, for any nonsingular affine variety over a perfect field of characteristic p. We then compare these cohomology groups with overconvergent de Rham-Witt cohomology. It was shown earlier that if the affine variety has small dimension relative to the characteristic of the ground field, then the cohomology groups are isomorphic. We extend this result to show that for any nonsingular affine variety, regardless of dimension, we have an isomorphism between integral Monsky-Washnitzer cohomology and overconvergent de Rham-Witt cohomology in degrees which are small relative to the characteristic.
U2 - 10.4310/MRL.2014.v21.n2.a6
DO - 10.4310/MRL.2014.v21.n2.a6
M3 - Journal article
VL - 21
SP - 281
EP - 288
JO - Mathematical Research Letters
JF - Mathematical Research Letters
SN - 1073-2780
IS - 2
ER -
ID: 64396600