Subfields of ample fields : rational maps and definability

Fehm, Arno

Subfields of ample fields : rational maps and definability

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Datum

2010

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Algebra. 2010, 323(6), pp. 1738-1744. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2009.11.037

Zusammenfassung

Pop proved that a smooth curve C over an ample field K with C(K)≠empty set has |K| many rational points. We strengthen this result by showing that there are |K| many rational points that do not lie in a given proper subfield, even after applying a rational map. This has several consequences. For example, we gain insight into the structure of existentially definable (i.e. diophantine) subsets of ample fields.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Ample field, Rational point, Algebraic curve, Definability

Zitieren

ISO 690

FEHM, Arno, 2010. Subfields of ample fields : rational maps and definability. In: Journal of Algebra. 2010, 323(6), pp. 1738-1744. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2009.11.037

BibTex

@article{Fehm2010Subfi-12745,
  year={2010},
  doi={10.1016/j.jalgebra.2009.11.037},
  title={Subfields of ample fields : rational maps and definability},
  number={6},
  volume={323},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={1738--1744},
  author={Fehm, Arno}
}

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