The arc-topology

Mardi 14 janvier 14:00-15:15 - Akhil Mathew - Université de Chicago et IHES

Résumé : 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 <=1 valuation rings.
This topology is motivated by classical questions in algebraic
K-theory. Our main result is that étale 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.

Lieu : salle 3L15 bâtiment 307

The arc-topology  Version PDF