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arXiv · 1701.04867

\'Etale homotopy groups of algebraic groups and homogeneous spaces

Cyril Demarche·Tamás Szamuely
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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.

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Cyril Demarche, Tamás Szamuely. 2017-01-17. \'Etale homotopy groups of algebraic groups and homogeneous spaces. https://arxiv.org/abs/1701.04867

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