Geodesic
The pro-étale topos as a category of pyknotic presheaves
Documenta mathematica, Tome 27 (2022), pp. 2067-2106 Cet article a éte moissonné depuis la source EMS Press

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In this paper we will show that for a quasicompact quasiseparated scheme X the hypercomplete pro-étale ∞-topos, as introduced by Bhatt and Scholze, is equivalent to the ∞-category of continuous representations of the Galois category Gal(X) of X with values in the ∞-category of pyknotic spaces. In particular this proves that internally to pyknotic spaces, the hypercomplete pro-étale ∞-topos of X is an ∞-category of presheaves.
DOI : 10.4171/dm/x26
Classification : 14F20, 18F10
Mots-clés : pro-étale topology, exodromy 
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     author = {Sebastian Wolf},
     title = {The pro-\'etale topos as a category of pyknotic presheaves},
     journal = {Documenta mathematica},
     pages = {2067--2106},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x26},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x26/}
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Sebastian Wolf. The pro-étale topos as a category of pyknotic presheaves. Documenta mathematica, Tome 27 (2022), pp. 2067-2106. doi: 10.4171/dm/x26

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