Artin–Mazur–Milne duality for fppf cohomology

Demarche, Cyril; Harari, David

doi:10.2140/ant.2019.13.2323

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Artin–Mazur–Milne duality for fppf cohomology

Cyril Demarche and David Harari

Vol. 13 (2019), No. 10, 2323–2357

DOI: 10.2140/ant.2019.13.2323

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

Vol. 13, No. 10, 2019