Vol. 13, No. 10, 2019

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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