On some finiteness results for unramified cohomology

TL;DR

This paper establishes finiteness results for unramified cohomology of function fields over various fields, broadening understanding of algebraic varieties' cohomological properties.

Contribution

It provides new finiteness theorems for unramified cohomology over fields of type (F'_m), including several important classes of fields.

Findings

Finiteness results for unramified cohomology over algebraically closed fields

Finiteness results over finite and local fields

Extension to higher local fields of characteristic 0

Abstract

We obtain several finiteness results for the unramified cohomology of function fields of algebraic varieties defined over fields of type (F'_m), a class that includes algebraically closed fields, finite fields, local fields, and some higher local fields of characteristic 0.