The pro-étale topology for schemes

Bhargav Bhatt; Peter Scholze

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arXiv · 1309.1198

The pro-étale topology for schemes

Bhargav Bhatt·Peter Scholze

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Abstract

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-étale topology, which is a Grothendieck topology on schemes that is closely related to the étale 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.

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BibTeX RIS

Bhargav Bhatt, Peter Scholze. 2014-12-17. The pro-étale topology for schemes. https://arxiv.org/abs/1309.1198

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