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Magnus Carlson: Étale homotopy, pro-categories and obstruction theory.

Tid: Ti 2013-09-24 kl 15.15 - 17.00

Plats: KTH, room 3418

In the 60s, Artin-Maur defined the étale homotopy type of a scheme which captures a lot of homotopical information of the scheme. Recently, Barnea-Schlank showed how one could construct the étale homotopy type in a natural way as a derived functor. The power of this approach is that it leads itself to generaliations and allows us to define new cousins to the étale homotopy type, such as a flat homotopy type. I will try to give an overview of how the étale homotopy type is constructed as a derived functor, explain how this connects the study of obstructions to solutions for diophantine equations to the theory of obstructions for sections of a fiber bundle. Given time, I will also talk about some conjectures that have been made by Schlank on the flat homotopy type.