Integral Comparison of Monsky-Washnitzer and overconvergent de Rham-Witt cohomology

TL;DR

This paper extends the comparison between integral Monsky-Washnitzer and overconvergent de Rham-Witt cohomology to all cohomological degrees for smooth varieties over perfect fields of positive characteristic, regardless of dimension or prime.

Contribution

It generalizes previous results by establishing an integral comparison across all degrees, independent of dimension and prime, for smooth varieties over perfect fields of characteristic p.

Findings

Extended the comparison to all cohomological degrees

Independence from dimension and prime p established

Unified the cohomology comparison framework

Abstract

The goal of this small note is to extend a result by Christopher Davis and David Zureick-Brown on the comparison between integral Monsky-Washnitzer cohomology and overconvergent de~Rham-Witt cohomology for a smooth variety over a perfect field of positive characteristic $p$ to all cohomological degrees independent of the dimension of the base or the prime number $p$. Le but de ce travail est de prolonger un r\'esultat de Christopher Davis et David Zureick-Brown concernant la comparaison entre la cohomologie de Monsky-Washnitzer enti\`ere et la cohomologie de de~Rham-Witt surconvergente d'une vari\'et\'e lisse sur un coprs parfait de charact\'eristique positive $p$ \`a tous les degr\'es cohomologiques ind\'epnedent de la dimension de base et du nombre premier $p$.