Subfields of ample fields I. Rational maps and definability
Algebraic Geometry
2008-11-19 v1 Logic
Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0811.2895,
title = {Subfields of ample fields I. Rational maps and definability},
author = {Arno Fehm},
journal= {arXiv preprint arXiv:0811.2895},
year = {2008}
}
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8 pages