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

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