Ambrus Pal: Simplicial homotopy theory of algebraic varieties over real closed fields

Coffee: 14:30-15:00
 
Abstract: First I will introduce the homotopy type of the simplicial set of continuous definable simplexes of an algebraic variety defined over a real closed field, which I call the real homotopy type. Then I will talk about the analogue of the theorems of Artin-Mazur and Cox comparing the real homotopy type with the étale homotopy type, as well as an analogue of Sullivan's conjecture which together imply a homotopy version of Grothendieck's section conjecture. As an application I show that for example for rationally connected varieties over any real closed fields the map from connected components of points to homotopy fixed points is a bijection.