On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq

Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points grows by taking finite extensions of the base field. We also investigate the...

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Detalles Bibliográficos
Autores: Miret, Josep M. (Josep Maria), Pujolàs Boix, Jordi, Valera Martín, Javier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/48929
Acceso en línea:https://doi.org/10.1007/s00013-015-0798-6
http://hdl.handle.net/10459.1/48929
Access Level:acceso abierto
Palabra clave:Elliptic curve
Finite field
Group order
ℓ-adic valuation
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spelling On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of FqMiret, Josep M. (Josep Maria)Pujolàs Boix, JordiValera Martín, JavierElliptic curveFinite fieldGroup orderℓ-adic valuationLet E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points grows by taking finite extensions of the base field. We also investigate the group structure of the corresponding l-Sylow subgroups.The authors would like to thank the anonymous referee, whose comments highly improved the quality of this publication. The research of the authors was supported in part by the Grants MTM2013-46949-P (Spanish Ministerio de Ciencia e Innovaci´on), 2014SGR-1666 (Generalitat de Catalunya).Springer Verlag2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttps://doi.org/10.1007/s00013-015-0798-6http://hdl.handle.net/10459.1/48929reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)InglésMINECO/PN2013-2016/MTM2013-46949-PVersió postprint del document publicat a https://doi.org/10.1007/s00013-015-0798-6Archiv der Mathematik, 2015, vol.105, núm. 3, p. 261-269(c) Springer Basel, 2015info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/489292026-06-24T12:42:17Z
dc.title.none.fl_str_mv On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
title On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
spellingShingle On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
Miret, Josep M. (Josep Maria)
Elliptic curve
Finite field
Group order
ℓ-adic valuation
title_short On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
title_full On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
title_fullStr On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
title_full_unstemmed On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
title_sort On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq
dc.creator.none.fl_str_mv Miret, Josep M. (Josep Maria)
Pujolàs Boix, Jordi
Valera Martín, Javier
author Miret, Josep M. (Josep Maria)
author_facet Miret, Josep M. (Josep Maria)
Pujolàs Boix, Jordi
Valera Martín, Javier
author_role author
author2 Pujolàs Boix, Jordi
Valera Martín, Javier
author2_role author
author
dc.subject.none.fl_str_mv Elliptic curve
Finite field
Group order
ℓ-adic valuation
topic Elliptic curve
Finite field
Group order
ℓ-adic valuation
description Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points grows by taking finite extensions of the base field. We also investigate the group structure of the corresponding l-Sylow subgroups.
publishDate 2015
dc.date.none.fl_str_mv 2015
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1007/s00013-015-0798-6
http://hdl.handle.net/10459.1/48929
url https://doi.org/10.1007/s00013-015-0798-6
http://hdl.handle.net/10459.1/48929
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv MINECO/PN2013-2016/MTM2013-46949-P
Versió postprint del document publicat a https://doi.org/10.1007/s00013-015-0798-6
Archiv der Mathematik, 2015, vol.105, núm. 3, p. 261-269
dc.rights.none.fl_str_mv (c) Springer Basel, 2015
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Basel, 2015
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
repository.name.fl_str_mv
repository.mail.fl_str_mv
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