Parimala, R. Homogeneous varieties – zero-cycles of degree one versus rational points. (English) Zbl 1095.14018 Asian J. Math. 9, No. 2, 251-256 (2005). 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. Reviewer: T. G. Berry (Caracas) Cited in 1 ReviewCited in 13 Documents MSC: 14G05 Rational points 14L30 Group actions on varieties or schemes (quotients) 14M17 Homogeneous spaces and generalizations Keywords:homogeneous variety; zero-cycle; rational point PDFBibTeX XMLCite \textit{R. Parimala}, Asian J. Math. 9, No. 2, 251--256 (2005; Zbl 1095.14018) Full Text: DOI