# The Pro-\'Etale Topos as a Category of Pyknotic Presheaves

@inproceedings{Wolf2020ThePT, title={The Pro-\'Etale Topos as a Category of Pyknotic Presheaves}, author={Sebastian Johannes Wolf}, year={2020} }

. In this paper we will show that for a coherent scheme 𝑋 the hypercomplete pro-étale ∞ -topos, as introduced by Bhatt and Scholze, is equivalent to the category of con- tinuous 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 hyper- complete pro-étale ∞ -topos of 𝑋 is a category of presheaves.

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