The arc-topology -- Akhil Mathew, July 22, 2020.

Abstract: 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.