Subfields of ample fields I. Rational maps and definability

Simple item page
dc.creatorFehm, Arno
dc.date2008-11-18
dc.date.accessioned2026-07-07T10:19:10Z
dc.date.available2026-07-07T10:19:10Z
dc.descriptionPop 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0811.2895
dc.identifierhttp://arxiv.org/abs/0811.2895
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174411
dc.subjectAlgebraic Geometry
dc.subjectLogic
dc.subjectNumber Theory
dc.subject12E30; 14G05; 12F99; 03C60
dc.titleSubfields of ample fields I. Rational maps and definability
dc.typetext

Files

Collections

arXiv