\'Etale homotopy groups of algebraic groups and homogeneous spaces
Algebraic Geometry
2022-06-23 v2
Abstract
We show the vanishing of the second homotopy group of the \'etale homotopy type of a smooth connected algebraic group over a separably closed field, completed away from the characteristic. This is an algebraic analogue of a classical theorem of Elie Cartan. Based on this result, we establish an explicit formula for the similarly completed second homotopy group of a homogeneous space.
Keywords
Cite
@article{arxiv.1701.04867,
title = {\'Etale homotopy groups of algebraic groups and homogeneous spaces},
author = {Cyril Demarche and Tamás Szamuely},
journal= {arXiv preprint arXiv:1701.04867},
year = {2022}
}
Comments
v2: major revision, some inaccurate statements in the first version corrected