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Homogeneous varieties – zero-cycles of degree one versus rational points. (English) Zbl 1095.14018

The paper first surveys open questions as to whether various types of varieties homogeneous under a linear algebraic group which have degree 1 zero-cycles have rational points. The second section gives a construction of projective homogeneous varieties over the field of Laurent series over \(p\)-adic fields which admit zero-cycles of degree 1 but which have no rational points, thus answering one of these questions in the negative.

MSC:

14G05 Rational points
14L30 Group actions on varieties or schemes (quotients)
14M17 Homogeneous spaces and generalizations
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