BIRS Workshop Lecture Videos
Galois Equivariant Ã tale Realization Carchedi, David
Ã 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 Ã©tale realization functor of Isaksen, which provides a bridge between unstable motivic homotopy theory and Ã©tale 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.
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