• Corpus ID: 229340123

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

  title={The Pro-\'Etale Topos as a Category of Pyknotic Presheaves},
  author={Sebastian Johannes Wolf},
  • S. Wolf
  • Published 18 December 2020
  • Mathematics
. 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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