colliot@math.u-psud.fr, gille@math.u-psud.fr, parimala@math.tifr.res.in

Submission: 2003, Mar 10

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. To any such field one associates completions with respect to a natural family of discrete valuations of K. We show that homogeneous spaces of connected linear algebraic groups over such a field K satisfy most properties familiar in the context of number fields: Hasse principle, finiteness of R-equivalence. This paper will appear in the Duke Mathematical Journal

2000 Mathematics Subject Classification: 20G30

Keywords and Phrases: Galois cohomology, Linear algebraic groups, Function fields

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