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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-Grothendi‚Äčeck vanishing for affinoids in rigid analytic geometry, which strengthens results of Hansen.

This is joint work with Bhargav Bhatt.

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