Tom Bachmann: Motivic real étale homotopy theory revisited

An étale morphism X-Y of schemes is called a real étale covering if it induces a surjection on k-valued points, for real closed fields k. Following Coste, Roy, Knebusch, Scheiderer and many others, this defines a topology on schemes closely related to semialgebraic geometry. I will explain what happens when this topology is combined with A1-invariance. Specifically, I will explain why for any scheme S, the localization of P (SmS ) at A^1 equivalences and real étale equivalences is just the small real étale ∞-topos of S.