The Pro-étale Topology for Schemes

  title={The Pro-étale Topology for Schemes},
  author={Bhargav Bhatt},
ABSTRACT. We give a new definition of the derived category of constructible Q`-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 Q`-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… CONTINUE READING
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