Geodesic
The pro-étale topos as a category of pyknotic presheaves
Documenta mathematica, Tome 27 (2022), pp. 2067-2106.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper we will show that for a quasicompact quasiseparated scheme $X$ the hypercomplete pro-étale $\infty$-topos, as introduced by Bhatt and Scholze, is equivalent to the $\infty$-category of continuous representations of the Galois category $\mathrm{Gal}(X)$ of $X$ with values in the $\infty$-category of pyknotic spaces. In particular this proves that internally to pyknotic spaces, the hypercomplete pro-étale $\infty$-topos of $X$ is an $\infty$-category of presheaves.
Classification : 18F10, 14F20
Keywords: pro-étale topology, exodromy 
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     author = {Wolf, Sebastian},
     title = {The pro-\'etale topos as a category of pyknotic presheaves},
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Wolf, Sebastian. The pro-étale topos as a category of pyknotic presheaves. Documenta mathematica, Tome 27 (2022), pp. 2067-2106. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a13/