Deninger’s conjectures and Weil–Arakelov cohomology

We conjecture the existence of a long exact sequence relating Deninger’s conjectural cohomology to Weil–Arakelov cohomology, the latter being unconditionally defined. We prove this conjecture for smooth projective varieties over finite fields whose Weil-étale motivic cohomology groups are finitely g...

Authors: Flach, Matthias
Morin, Baptiste
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:05.01.2021
Source:Münster Journal of Mathematics, 13 (2020), S. 519-540
Publisher: Mathematisches Institut (Universität Münster)
Edition statement:[Electronic ed.]
DDC Subject:510: Mathematik
License:InC 1.0
Language:English
Format:PDF document
URN:urn:nbn:de:hbz:6-90169643343
Other Identifiers:URN: urn:nbn:de:hbz:6-90169643343
DOI: 10.17879/90169642993
Permalink:https://nbn-resolving.de/urn:nbn:de:hbz:6-90169643343
Digital documents:mjm_2020_13_519-540.pdf

We conjecture the existence of a long exact sequence relating Deninger’s conjectural cohomology to Weil–Arakelov cohomology, the latter being unconditionally defined. We prove this conjecture for smooth projective varieties over finite fields whose Weil-étale motivic cohomology groups are finitely generated. Then we explain the consequences that such an exact sequence would have.