Homogeneous varieties -- zero-cycles of degree one versus rational points
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.
scientific article; zbMATH DE number 5016085