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.

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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