Rationally connected varieties over local fields
Algebraic Geometry
2007-05-23 v2
Abstract
Let X be a smooth, projective variety defined over a local field K. Following Manin, two K-points of X are called R-equivalent if they can be joined by a rational curve defined over K. The main result of this note shows that if there are only finitely many R-equivalence classes over the algebraic closure of K then the same holds over K. This also yields the unirationality of several classes of varieties over K.
Cite
@article{arxiv.math/9901021,
title = {Rationally connected varieties over local fields},
author = {János Kollár},
journal= {arXiv preprint arXiv:math/9901021},
year = {2007}
}
Comments
11 pages, published version