Arithmetic of linear algebraic groups over certain fields of dimension two

Colliot-Thélène, Jean-Louis ; Gille, Philippe ; Parimala, Raman (2001) Arithmetic of linear algebraic groups over certain fields of dimension two Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, 333 (9). pp. 827-832. ISSN 0764-4442

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Official URL: http://dx.doi.org/10.1016/S0764-4442(01)02123-1

Related URL: http://dx.doi.org/10.1016/S0764-4442(01)02123-1

Abstract

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.

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