The Pro-Étale Topos as a Category of Pyknotic Presheaves

2020/12/18 by Sebastián Wolf, Wolf, Sebastian
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2012.10502

openalex publication_date 2020/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a coherent scheme and let Gal(X) denote the Galois category of X, as introduced by Barwick, Glasman and Haine. In this paper we prove that the hypercomplete pro-étale ∞-topos X_proet of X, introduced by Bhatt and Scholze, is equivalent to the category of continuous representations of Gal(X) with values in the ∞-category of pyknotic spaces.

Related

• Extended étale homotopy groups from profinite Galois categories
• The pro-étale topology for algebraic stacks
• A pro-cdh topology on formal schemes
• The Pro-Étale Homotopy Type
• A Projective Model Structure on Pro Simplicial Sheaves, and the Relative\n 'Etale Homotopy Type