The arc-topology 
-- Akhil Mathew, September 21, 2018

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I will discuss a Grothendieck topology on the category of
quasi-compact quasi-separated schemes called the "arc-topology."
Covers in the arc-topology are tested via rank \leq 1 valuation rings.
This topology is motivated by classical questions in algebraic
K-theory. Our main result is that \'etale cohomology with torsion
coefficients satisfies arc-descent. Using these tools, I will describe
an application to Artin-Grothendieck vanishing in rigid analytic
geometry, which strengthens results of Hansen. This is joint work with
Bhargav Bhatt.