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- W4213291016 abstract "Publisher SummaryThis chapter describes the quantitative aspect of the local-global principle—the question of when the elements of local groups and their products can be approximated with any given accuracy by the elements. Strong approximation (that is, approximation using elements which satisfy certain integral conditions) applies only to global fields. The chapter defines weak, as well as strong approximation for arbitrary algebraic varieties. The existing methods are essentially based on the analysis of the group structure on the set of rational points. The chapter presents the approximation results and discusses the Kneser-Tits hypothesis on isotropic groups. The structure theory of linear algebraic groups provides an exhaustive description of the structure of an algebraic group G over an algebraically closed field. The Kneser-Tits conjecture is true for K algebraically closed. The case K = R is the only one in which the proof of the Kneser-Tits conjecture is based on the general structural considerations." @default.
- W4213291016 created "2022-02-24" @default.
- W4213291016 date "1994-01-01" @default.
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- W4213291016 title "7. Approximation in Algebraic Groups" @default.
- W4213291016 doi "https://doi.org/10.1016/s0079-8169(08)62072-3" @default.
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