Rationally connected varieties over local fields

Details Rationally connected varieties over local fields Rationally connected varieties over local fields

1999-01-06

arxiv.org/abs/math/9901021v2

Ann. of Math. (2) 150 (1999), no. 1, 357-367

Mathematics

Algebraic Geometry

11 pages, published version

Scientific paper

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.

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