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Algebra and Geometry Seminar

Monday, January 14, 2019
4:00pm to 5:00pm
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Linde Hall 387
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.

For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at [email protected].