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...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/65082 |
| Acesso em linha: | https://doi.org/10.1142/S0219498819501354 http://hdl.handle.net/10459.1/65082 |
| Access Level: | acceso abierto |
| Palavra-chave: | Jacobians of genus 2 curves Finite fields Cardinality 2-adic valuation |
| Resumo: | 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). |
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