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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
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