Mathieu Florence: Rational points on homogeneous spaces and their compactifications

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:

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