On computation of unramified cohomology over non-closed fields

Wenhao Li

On computation of unramified cohomology over non-closed fields

Algebraic Geometry 2026-06-27 v1

Authors: Wenhao Li

Abstract

We give examples of varieties $X$ defined over a non-algebraically closed field $k$ with nontrivial unramified cohomology, in the case when the field $k$ is of bounded cohomological dimension, or the variety $X$ is a conic bundle over a rational surface and $k$ is an arbitrary field of characteristic different from $2$ .

Keywords

unramified cohomology non-closed fields conic bundles cohomological dimension rational surfaces

Cite

@article{arxiv.2606.29107,
  title  = {On computation of unramified cohomology over non-closed fields},
  author = {Wenhao Li},
  journal= {arXiv preprint arXiv:2606.29107},
  year   = {2026}
}