Subfields of ample fields I. Rational maps and definability
Fehm, Arno
arXiv, 0811.2895 / Harvested from arXiv
Text on arXiv
Pop proved that a smooth curve C over an ample field K that has a K-rational point has |K| many K-rational points. We strengthen this result by showing that there are |K| many K-rational points that do not lie in a given proper subfield, even after applying a rational map. As a consequence we gain insight into the structure of existentially definable subsets of ample fields. In particular, we prove that a perfect ample field has no existentially definable proper infinite subfields.
Publié le : 2008-11-18
Classification:  Mathematics - Algebraic Geometry,  Mathematics - Logic,  Mathematics - Number Theory,  12E30,  14G05,  12F99,  03C60 
@article{0811.2895,
     author = {Fehm, Arno},
     title = {Subfields of ample fields I. Rational maps and definability},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0811.2895}
}

Fehm, Arno. Subfields of ample fields I. Rational maps and definability. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0811.2895/