On the rank of abelian varieties over ample fields

Zitieren

Dateien zu dieser Ressource

Dateien Größe Format Anzeige

Zu diesem Dokument gibt es keine Dateien.

FEHM, Arno, Sebastian PETERSEN, 2010. On the rank of abelian varieties over ample fields. In: International Journal of Number Theory. 06(03), pp. 579-586. ISSN 1793-0421. Available under: doi: 10.1142/S1793042110003071

@article{Fehm2010abeli-12746, title={On the rank of abelian varieties over ample fields}, year={2010}, doi={10.1142/S1793042110003071}, number={03}, volume={06}, issn={1793-0421}, journal={International Journal of Number Theory}, pages={579--586}, author={Fehm, Arno and Petersen, Sebastian} }

<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/12746"> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-08-15T09:52:20Z</dc:date> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:language>eng</dc:language> <dc:contributor>Fehm, Arno</dc:contributor> <dcterms:issued>2010</dcterms:issued> <dcterms:bibliographicCitation>First publ. in: International Journal of Number Theory 6 (2010), 3, pp. 579-586</dcterms:bibliographicCitation> <dcterms:abstract xml:lang="eng">A field K is called ample if every smooth K-curve that has a K-rational point has infinitely many of them. We prove two theorems to support the following conjecture, which is inspired by classical infinite rank results: Every non-zero Abelian variety A over an ample field K which is not algebraic over a finite field has infinite rank. First, the ℤ(p)-module A(K) ⊗ ℤ(p) is not finitely generated, where p is the characteristic of K. In particular, the conjecture holds for fields of characteristic zero. Second, if K is an infinite finitely generated field and S is a finite set of local primes of K, then every Abelian variety over K acquires infinite rank over certain subfields of the maximal totally S-adic Galois extension of K. This strengthens a recent infinite rank result of Geyer and Jarden.</dcterms:abstract> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dc:rights>deposit-license</dc:rights> <dcterms:title>On the rank of abelian varieties over ample fields</dcterms:title> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-08-15T09:52:20Z</dcterms:available> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/12746"/> <dc:creator>Fehm, Arno</dc:creator> <dc:contributor>Petersen, Sebastian</dc:contributor> <dc:creator>Petersen, Sebastian</dc:creator> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> </rdf:Description> </rdf:RDF>

Das Dokument erscheint in:

KOPS Suche


Stöbern

Mein Benutzerkonto