Vol. 13, No. 10, 2019

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

Volume 13
Issue 10, 2243–2434
Issue 9, 1983–2242
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

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
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Artin–Mazur–Milne duality for fppf cohomology

Cyril Demarche and David Harari

Vol. 13 (2019), No. 10, 2323–2357
Abstract

We provide a complete proof of a duality theorem for the fppf cohomology of either a curve over a finite field or a ring of integers of a number field, which extends the classical Artin–Verdier Theorem in étale cohomology. We also prove some finiteness and vanishing statements.

Keywords
fppf cohomology, arithmetic duality, Artin approximation theorem
Mathematical Subject Classification 2010
Primary: 11G20
Secondary: 14H25
Milestones
Received: 1 May 2018
Revised: 3 July 2019
Accepted: 1 August 2019
Published: 6 January 2020
Authors
Cyril Demarche
Institut de Mathématiques de Jussieu-Paris Rive Gauche
Sorbonne Université
Paris
France
David Harari
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud
Orsay
France