Vol. 10, No. 8, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Syntomic cohomology and $p$-adic regulators for varieties over $p$-adic fields

Jan Nekovář and Wiesława Nizioł

Appendix: Laurent Berger and Frédéric Déglise

Vol. 10 (2016), No. 8, 1695–1790
Abstract

We show that the logarithmic version of the syntomic cohomology of Fontaine and Messing for semistable varieties over p-adic rings extends uniquely to a cohomology theory for varieties over p-adic fields that satisfies h-descent. This new cohomology — syntomic cohomology — is a Bloch–Ogus cohomology theory, admits a period map to étale cohomology, and has a syntomic descent spectral sequence (from an algebraic closure of the given field to the field itself) that is compatible with the Hochschild–Serre spectral sequence on the étale side and is related to the Bloch–Kato exponential map. In relative dimension zero we recover the potentially semistable Selmer groups and, as an application, we prove that Soulé’s étale regulators land in the potentially semistable Selmer groups.

Our construction of syntomic cohomology is based on new ideas and techniques developed by Beilinson and Bhatt in their recent work on p-adic comparison theorems.

Keywords
syntomic cohomology, regulators
Mathematical Subject Classification 2010
Primary: 14F30
Secondary: 11G25
Milestones
Received: 26 February 2016
Accepted: 5 July 2016
Published: 7 October 2016
Authors
Jan Nekovář
Institut de Mathématiques de Jussieu
Université Pierre et Marie Curie (Paris 6)
75252 Paris Cedex 05
France
Wiesława Nizioł
École Normale Supérieure de Lyon
Unité de Mathématiques Pures et Appliquées
69364 Lyon Cedex 07
France
Laurent Berger
École Normale Supérieure de Lyon
Unité de Mathématiques Pures et Appliquées
69364 Lyon Cedex 07
France
Frédéric Déglise
École Normale Supérieure de Lyon
Unité de Mathématiques Pures et Appliquées
69364 Lyon Cedex 07
France