Overconvergent de Rham–Witt cohomology for semi-stable varieties

We define an overconvergent version of the Hyodo–Kato complex for semi-stable varieties Y over perfect fields of positive characteristic, and prove that its hypercohomology tensored with Q recovers the log-rigid cohomology when Y is quasi-projective. We then describe the monodromy operator using the...

Authors: Gregory, Oliver
Langer, Andreas
Further contributors: Deninger, Christopher (Honoree)
Division/Institute:FB 10: Mathematik und Informatik
Document types:Article
Media types:Text
Publication date:2020
Date of publication on miami:24.08.2020
Modification date:05.01.2023
Source:Münster Journal of Mathematics, 13 (2020), S. 541-571
Publisher: Mathematisches Institut (Universität Münster)
Edition statement:[Electronic ed.]
DDC Subject:510: Mathematik
License:InC 1.0
Language:Englisch
Format:PDF document
URN:urn:nbn:de:hbz:6-90169635796
Other Identifiers:DOI: 10.17879/90169635144
Permalink:https://nbn-resolving.de/urn:nbn:de:hbz:6-90169635796
Digital documents:mjm_2020_13_541-571.pdf

We define an overconvergent version of the Hyodo–Kato complex for semi-stable varieties Y over perfect fields of positive characteristic, and prove that its hypercohomology tensored with Q recovers the log-rigid cohomology when Y is quasi-projective. We then describe the monodromy operator using the overconvergent Hyodo–Kato complex. Finally, we show that overconvergent Hyodo–Kato cohomology agrees with log-crystalline cohomology in the projective semi-stable case.