arXiv 1701.048672017-01math.AG

Étale homotopy groups of algebraic groups and homogeneous spaces

Cyril Demarche, Tamás Szamuely

备注：: v2: major revision, some inaccurate statements in the first version corrected

英文摘要：

We show the vanishing of the second homotopy group of the étale 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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