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Arithmetic of linear algebraic groups over certain fields of dimension two. (Arithmétique des groupes algébriques linéaires sur certains corps géométriques de dimension deux.) (French. Abridged English version) Zbl 1037.20050

Summary: Let \(k\) be an algebraically closed field of characteristic zero. Let \(K\) be either a function field in two variables over \(k\) or the fraction field of a 2-dimensional, excellent, strictly Henselian local domain with residue field \(k\). We show that linear algebraic groups over such a field \(K\) satisfy most properties familiar in the context of number fields: finiteness of \(R\)-equivalence, Hasse principle for complete homogeneous spaces.

MSC:

20G30 Linear algebraic groups over global fields and their integers
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