On schemes with trivial higher \'etale homotopy groups

Mohammed Moutand

On schemes with trivial higher \'etale homotopy groups

Algebraic Geometry 2026-02-27 v2

Authors: Mohammed Moutand

Abstract

Let $(X,\bar x)$ be a pointed connected noetherian scheme. In this note, we give characterizations for the vanishing of the second \'etale homotopy group $\pi^{\rm \'et}_2(X,\bar x)$ in terms of splitting profinite-\'etale covers of $X$ , and by means of universal covering spaces of the Artin-Mazur-Friedlander \'etale homotopy type $Et(X)$ . In particular, this provides certain classes of schemes for which the Brauer map is surjective.

Keywords

étale homotopy group noetherian scheme profinite-étale cover Brauer map Artin-Mazur-Friedlander étale homotopy type

Cite

@article{arxiv.2312.08505,
  title  = {On schemes with trivial higher \'etale homotopy groups},
  author = {Mohammed Moutand},
  journal= {arXiv preprint arXiv:2312.08505},
  year   = {2026}
}

On schemes with trivial higher \'etale homotopy groups

Abstract

Keywords

Cite

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