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Proceedings of the American Mathematical Society Series B

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Integral comparison of Monsky–Washnitzer and overconvergent de Rham–Witt cohomology


Authors: Veronika Ertl and Johannes Sprang
Journal: Proc. Amer. Math. Soc. Ser. B 5 (2018), 64-72
MSC (2010): Primary 14F30; Secondary 14F40, 13K05
DOI: https://doi.org/10.1090/bproc/38
Published electronically: November 14, 2018
MathSciNet review: 3876137
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Abstract:

The goal of this short 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 $p$.

Résumé. Le but de ce travail est de prolonger un résultat de Christopher Davis et David Zureick-Brown concernant la comparaison entre la cohomologie de Monsky–Washnitzer entière et la cohomologie de de Rham–Witt surconvergente d’une variété lisse sur un corps parfait de charactéristique positive $p$ à tous les degrés cohomologiques indépendent de la dimension de base et du nombre premier $p$.


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Additional Information

Veronika Ertl
Affiliation: Fakultät für Mathematik, Universität Regensburg, 93053 Regensburg, Germany
MR Author ID: 1169710

Johannes Sprang
Affiliation: Fakultät für Mathematik, Universität Regensburg, 93053 Regensburg, Germany
MR Author ID: 1038054

Keywords: Monsky–Washnitzer cohomology, de Rham–Witt complex, overconvergent
Received by editor(s): April 6, 2018
Received by editor(s) in revised form: July 10, 2018, and July 16, 2018
Published electronically: November 14, 2018
Additional Notes: The first author was supported by a habilitation grant through the Bavarian government.
The second author was supported by DFG through CRC 1085.
Communicated by: Rachel Pries
Article copyright: © Copyright 2018 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)