The pro-étale topos as a category of pyknotic presheaves (Q2695701)

Summary: 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.