On Galois cohomology and weak approximation of connected reductive groups over fields of positive characteristic (Q764650)

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 \textit{R. E. Kottwitz} [Duke Math. J. 51, 611--650 (1984; Zbl 0576.22020) and Math. Ann. 275, 365--399 (1986; Zbl 0577.10028)] and \textit{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.