Truncated pushforwards and refined unramified cohomology

Abstract

For a large class of cohomology theories, we prove that refined unramified cohomology is canonically isomorphic to the hypercohomology of a natural truncated complex of Zariski sheaves. This generalizes a classical result of Bloch and Ogus and solves a conjecture of Kok and Zhou.

21 pages, final version, to appear in Advances in Mathematics, updated some references and added Corollaries 1.4, 5.1, and 5.2