Artin-Mazur-Milne duality for fppf cohomology

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.

arXiv comment34 pages

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Cited by in corpus (7)

• Duality for cohomology of curves with coefficients in abelian varieties
• Arithmetics of homogeneous spaces over $p$-adic function fields
• Duality for complexes of tori over a global field of positive characteristic
• Finiteness and cofiniteness of fine Selmer groups over function fields
• Massey products in the étale cohomology of number fields
• The étale cohomology ring of a punctured arithmetic curve
• On $\mu$-invariants and isogenies for abelian varieties over function fields