Colliot-Thélène, Jean-Louis; Gille, Philippe; Parimala, Raman 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 C. R. Acad. Sci., Paris, Sér. I, Math. 333, No. 9, 827-832 (2001). 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. Cited in 3 ReviewsCited in 3 Documents MSC: 20G30 Linear algebraic groups over global fields and their integers Keywords:function fields in two variables; quotient fields; Henselian local domains; linear algebraic groups × Cite Format Result Cite Review PDF Full Text: DOI