The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields

Given a genus 2 curve C defined over a finite field Fq of odd characteristic such that 2|#Jac(C)(Fq), we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a tower of quadratic extensions of Fq. In the cases of simpler regularity, we determine the exponents of the 2-Syl...

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Detalles Bibliográficos
Autores: Garra Oronich, Ricard, Miret, Josep M. (Josep Maria), Pujolàs Boix, Jordi, Thériault, Nicolas
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/65082
Acceso en línea:https://doi.org/10.1142/S0219498819501354
http://hdl.handle.net/10459.1/65082
Access Level:acceso abierto
Palabra clave:Jacobians of genus 2 curves
Finite fields
Cardinality
2-adic valuation
Descripción
Sumario:Given a genus 2 curve C defined over a finite field Fq of odd characteristic such that 2|#Jac(C)(Fq), we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a tower of quadratic extensions of Fq. In the cases of simpler regularity, we determine the exponents of the 2-Sylow subgroup of Jac(C)(Fq2k).