Truncated pushforwards and refined unramified cohomology

TL;DR

This paper proves that for many cohomology theories, refined unramified cohomology aligns with hypercohomology of a specific sheaf complex, extending classical results and resolving a conjecture.

Contribution

It establishes a canonical isomorphism between refined unramified cohomology and hypercohomology of a truncated sheaf complex, generalizing prior work and solving a conjecture.

Findings

Refined unramified cohomology is isomorphic to hypercohomology of a truncated sheaf complex.

Generalizes classical results of Bloch and Ogus.

Solves a conjecture of Kok and Zhou.

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.