Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex

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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

Davis, CJ & Zureick-Brown, D 2014, 'Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex', Mathematical Research Letters, bind 21, nr. 2, s. 281 – 288. https://doi.org/10.4310/MRL.2014.v21.n2.a6

APA

Davis, C. J., & Zureick-Brown, D. (2014). Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex. Mathematical Research Letters, 21(2), 281 – 288. https://doi.org/10.4310/MRL.2014.v21.n2.a6

Vancouver

Davis CJ, Zureick-Brown D. Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex. Mathematical Research Letters. 2014;21(2):281 – 288. https://doi.org/10.4310/MRL.2014.v21.n2.a6

Author

Davis, Christopher James ; Zureick-Brown, David. / Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex. I: Mathematical Research Letters. 2014 ; Bind 21, Nr. 2. s. 281 – 288.

Bibtex

@article{be7301ab5aec46459ee855b973c81e54,
title = "Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex",
abstract = "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.",
author = "Davis, {Christopher James} and David Zureick-Brown",
year = "2014",
doi = "10.4310/MRL.2014.v21.n2.a6",
language = "English",
volume = "21",
pages = "281 – 288",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "Mathematical Publishing",
number = "2",

}

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