The pro-étale topology for schemes

By B. Bhatt, Peter Scholze. Astérisque, 2013

263 citations recorded by the source corpus.

We give a new definition of the derived category of constructible $\ell$-adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamental group of schemes, which is large enough to see all lisse $\ell$-adic sheaves, even on non-normal schemes. To accomplish these tasks, we define and study the pro-\'etale topology, which is a Grothendieck topology on schemes that is closely related to the \'etale topology, and yet better suited for infinite constructions typically encountered in $\ell$-adic cohomology. An essential foundational result is that this site is locally contractible in a well-defined sense.

Subfields: Geometry and Topology, Mathematical Physics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/00ee35a9d2501f76fc56aee27269f6699a2a2234

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Citations in the corpus

Relative p-adic Hodge theory, II: Imperfect period rings (2016, methodology): “We adapt to perfectoid spaces a construction for perfect schemes originating in [15].”
Hyperdescent and étale K-theory (2019, methodology): “f Example 4.4 again, we ﬁnd a natural equivalence PShΠ(TG,D) = Fun(O(G)op,D) ≃lim ←− N Fun(O(G/N)op,D). We next describe the Postnikov sheaﬁﬁcation following a method motivated by the pro-´etale site [BS15], cf. also subsection 2.3. This can be done without any extra ﬁniteness assumptions either on ”