Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-08T19:27:30.609Z Has data issue: false hasContentIssue false

A Duality Theorem for Étale p-Torsion Sheaves on Complete Varieties over a Finite Field

Published online by Cambridge University Press:  04 December 2007

THOMAS MOSER
Affiliation:
Oberstadt 23, 69198 Schriesheim/Germany. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be an arbitrary variety over a finite field k and p=char k,n∈ N. We will construct a complex of étale sheaves on X together with trace isomorphism from the highest étale cohomology group of this complex onto Z/p$^n$Z such that for every constructible Z/p$^n$Z-sheaf on X the Yoneda pairing is a nondegenerate pairing of finite groups. If X is smooth, this complex is the Gersten resolution of the logarithmic de Rham–Witt sheaf introduced by Gros and Suwa. The proof is based on the special case proven by Milne when the sheaf is constant and X is smooth, as well as on a purity theorem which in turn follows from a theorem about the cohomological dimension of C$_i$-fields due to Kato and Kuzumaki. If the existence of the Lichtenbaum complex is proven, the theorem will be the p-part of a general duality theorem for varieties over finite fields.

Type
Research Article
Copyright
© 1999 Kluwer Academic Publishers