Submission: 2004, Dec 22
Let k be a perfect field and G an algebraic group defined over k (we do not require G to be linear). Let X be a (right) homogeneous space of G. We show the following: if there exists a k-variety which is birational to X and which has a smooth k-rational point, then X also has a k-rational point.
2000 Mathematics Subject Classification:
Keywords and Phrases:
Full text: dvi.gz 30 k, dvi 72 k, ps.gz 579 k, pdf.gz 155 k, pdf 175 k.