Subfields of ample fields : rational maps and definability

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2010
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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.

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Fachgebiet (DDC)
510 Mathematik
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Ample field, Rational point, Algebraic curve, Definability
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undefined / . - undefined, undefined
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ISO 690FEHM, 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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