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18.09.2019
“Simplicial homotopy theory of algebraic varieties over real closed fields”

“Simplicial homotopy theory of algebraic varieties over real closed fields”

Ambrus Pal (Imperial College London)

Chebyshev Lab Seminar

Monday September 23 17:15 room 120 (14-th line V.O., 29)

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.

 

Everyone is welcome!