Artin-Mazur-Milne duality for fppf cohomology

TL;DR

This paper proves a duality theorem for fppf cohomology over curves and number rings, extending classical étale cohomology results, and establishes related finiteness and vanishing properties.

Contribution

It provides a complete proof of Artin-Mazur-Milne duality for fppf cohomology, extending classical results to new contexts.

Findings

Duality theorem for fppf cohomology over curves and number rings

Finiteness and vanishing results for cohomology groups

Extension of Artin-Verdier duality to fppf setting

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 \'etale cohomology. We also prove some finiteness and vanishing statements.