## On Galois cohomology and weak approximation of connected reductive groups over fields of positive characteristic.(English)Zbl 1254.11042

Let $$k$$ be a field, $$H^1(k, G)$$ be the functor from the category of linear algebraic groups $$G$$ over $$k$$ to the category of sets. This article considers various functors related to $$H^1(k, G)$$ and their relationships. When $$k$$ is a number field or $$k$$ is a field with char$$k =0$$, many results were proved in the papers of R. E. Kottwitz [Duke Math. J. 51, 611–650 (1984; Zbl 0576.22020) and Math. Ann. 275, 365–399 (1986; Zbl 0577.10028)] and J.-L. Colliot-Thelene [J. Reine Angew. Math. 618, 77–133 (2008; Zbl 1158.14021)]. The purpose of this article is to generalize these results to the case when $$k$$ is a function field of char$$k=p > 0$$. The detailed proof will appear elsewhere.

### MSC:

 11E72 Galois cohomology of linear algebraic groups 20G10 Cohomology theory for linear algebraic groups

### Citations:

Zbl 0576.22020; Zbl 0577.10028; Zbl 1158.14021
Full Text:

### References:

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