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Galois Equivariant à tale Realization

Banff International Research Station for Mathematical Innovation and Discovery

à tale homotopy theory, as originally introduced by Artin and Mazur in the late 60s, is a way of associating to a suitably nice scheme a pro-object in spaces. We will explain how, when working over a base field $k$, a modern reformulation in terms of the theory of infinity-topoi leads to a more refined invariant, which takes into account the action of the absolute Galois group. We will then explain joint work of ours with Elden Elmanto that extends the étale realization functor of Isaksen, which provides a bridge between unstable motivic homotopy theory and étale homotopy theory, to a functor taking into account the Galois group action. Time permitting, we will explain work in progress extending this to the stable setting.

Mathematics; Algebraic topology; Category theory; homological algebra

video/mp4

Author affiliation: George Mason University

2019-03-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69188

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/