\'Etale duality for constructible sheaves on arithmetic schemes

TL;DR

This paper establishes a duality theory for étale constructible sheaves on arithmetic schemes, linking étale homology and Gersten complexes, advancing the understanding of arithmetic duality principles.

Contribution

It introduces a unifying duality framework connecting étale sheaves, homology, and Gersten complexes on arithmetic schemes, which was not previously formulated.

Findings

Develops a general duality for étale constructible torsion sheaves.

Relates étale homology theory to Gersten-Bloch-Ogus-Kato complexes.

Provides foundational results used in subsequent research by the authors.

Abstract

In this note we relate three topics for arithmetic schemes: a general duality for \'etale constructible torsion sheaves, an \'etale homology theory, and a Gersten-Bloch-Ogus-Kato complex. The results in this paper have been used in other papers of the authors ([JS], [Sa], [SaH] in the list of references).