Elden Elmanto: Perfection in Motivic Homotopy Theory
Grothendieck proved that the small etale site is invariant under universal homeomorphism of schemes and calls this the "remarkable equivalence." The statement is false for Nisnevich/etale sheaves on big sites. However, after the inverting the residual characteristics, it turns out that the stable motivic homotopy category is. We will try to give a complete proof of this theorem, state some applications and future directions. This is joint work with A. A. Khan.