Algebra and Geometry Seminar

I will discuss a Grothendieck topology on the category of 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-Grothendi​eck vanishing for affinoids in rigid analytic geometry, which strengthens results of Hansen.

This is joint work with Bhargav Bhatt.