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Sebastian Bartling will speak on

On the étale cohomology of the Fargues-Fontaine curve

Abstract: From the point of view of étale cohomology we don’t know yet that the curve behaves like a classical curve (smooth projective, over an algebraically closed field). In this direction Laurent Fargues has made some conjectures: Vanishing of étale cohomology with constructible coefficients in degrees greater or equal than three, comparison with the étale cohomology of the adic curve and that the function field is C1. I´ll explain how to handle the vanishing and comparison in the easier case of l-torsion (l not p!) sheaves and outline a strategy how to attack the p-torsion case.