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

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  • Integral

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  • Christopher James Davis
  • David Zureick-Brown
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.
OriginalsprogEngelsk
TidsskriftMathematical Research Letters
Vol/bind21
Udgave nummer2
Sider (fra-til)281 – 288
Antal sider7
ISSN1073-2780
DOI
StatusUdgivet - 2014

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