Monday, January 14, 2019
4:00 PM -
5:00 PM
Linde Hall 387
Algebra and Geometry Seminar
The arc-topology
Akhil Mathew,
Department of Mathematics,
University of Chicago,
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-Grothendieck vanishing for affinoids in rigid analytic geometry, which strengthens results of Hansen.
This is joint work with Bhargav Bhatt.
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For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at [email protected].