Embeddings of function fields into ample fields
type: Item
instance of: scholarly article
title: Embeddings of function fields into ample fields
zbMATH Open document ID: 1261.12005
author: Arno Fehm
published in: Manuscripta Mathematica
publication date: 2011-02-17T00:00:00Z
review text: Let \(K\) be a field, \(V\) be a smooth \(K\)-variety and \(E\) be an ample field containing \(K.\) The author gives a necessary and sufficient condition for the existence of \(K\)-embedding of the function field \(K(V)\) into \(E\). The number of such embeddings is also computed. The author also investigates some aspects of the subfield structure of ample fields which leads to new examples of non-ample fields. Some connections between the existence of rational places on function fields and embeddings into ample fields are obtained; this connects the paper to an interesting problem raised by \textit{F. V. Kuhlmann} in [Adv. Math. 188, No. 2, 399--424 (2004; Zbl 1134.12304)], several equivalent versions of which are given.
reviewed by: Sudesh Kaur Khanduja
Mathematics Subject Classification ID: 12E30
Mathematics Subject Classification ID: 14H05
zbMATH DE Number: 5852702
zbMATH Keywords: field arithmetic
zbMATH Keywords: function fields
MaRDI profile type: Publication
full work available at URL: s00229-010-0415-8
OpenAlex ID: W1994162876
cites work: Characterization of extremal valued fields
cites work: Q4788752
cites work: Rational connectedness and Galois covers of the projective line
cites work: Q4944046
cites work: Q4364747
cites work: Subfields of ample fields. Rational maps and definability
cites work: ON THE RANK OF ABELIAN VARIETIES OVER AMPLE FIELDS
cites work: On the asymptotic behaviour of some towers of function fields over finite fields
cites work: On towers and composita of towers of function fields over finite fields
cites work: Non-PAC fields whose Henselian closures are separably closed
cites work: Regular split embedding problems over function fields of one variable over ample fields
cites work: On function fields with free absolute Galois groups
cites work: On ample fields
cites work: Schlanke Körper (Slim fields)
cites work: Defining transcendentals in function fields
cites work: The regular inverse Galois problem over non-large fields
cites work: Diophantine subsets of function fields of curves
cites work: Places of algebraic function fields in arbitrary characteristic
cites work: On Chevalley's Proof of Luroth's Theorem
cites work: Unramified covers of Galois covers of low genus curves
cites work: Gonality of modular curves in characteristic \(p\)
cites work: Embedding problems over large fields
cites work: Henselian implies large
cites work: Lectures on old and new results on algebraic curves
cites work: Unramified Skolem problems and unramified arithmetic Bertini theorems in positive characteristic
cites work: The uniform companion for large differential fields of characteristic 0
DOI: 10.1007/S00229-010-0415-8
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description: scientific article; zbMATH DE number 5852702