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

Autor:	Miret, Josep M. (Josep Maria), Pujolàs Boix, Jordi, Valera Martín, Javier
Předmět:	Group order Elliptic curve Finite field ℓ-adic valuation
Zdroj:	Recercat. Dipósit de la Recerca de Catalunya instname Repositorio Abierto de la UdL Universitad de Lleida
Popis:	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. 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).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::30dbb1347e99be4224cbcb236df7661e http://hdl.handle.net/10459.1/48929 Zobrazit plný text záznamu