Notes on étale cohomology of number fields

Abstract

In the setting of etale cohomology, M. Artin and J.-L.Verdier have proved a duality theorem for constructible abelian sheaves over the scheme Spec D, where D is the ring of integers in a number field {see [AV]).This duality theorem contains within it Tate duality for finite Galois modules over local and global fields, and is indeed the natural extension of Tate duality to the context of such schemes.In what follows, I would like to poke at this result from various angles, and make what I hope to be enlightening remarks and computations, so as to convey in a concrete way a sense of the information contained in this theorem.Rather than give its proof completely, I shall empha-( 1 ) This is an expository paper.

Locations

• Annales Scientifiques de l École Normale Supérieure - View - PDF