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

被引：0

作者：

Garra, Ricard

Miret, Josep M.

Pujolas, Jordi ^{[1
]}

Theriault, Nicolas

机构：

[1] Univ Lleida, Dept Matemat, Lleida, Spain

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2019年 / 18卷 / 07期

关键词：

Jacobians of genus 2 curves; finite fields; cardinality; 2-adic valuation; ABELIAN SURFACES; BISECTION;

D O I：

10.1142/S0219498819501354

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a genus 2 curve C defined over a finite field F-q of odd characteristic such that 2 vertical bar#Jac(C)(F-q), we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a tower of quadratic extensions of F-q. In the cases of simpler regularity, we determine the exponents of the 2-Sylow subgroup of Jac(C)(F-q2k).

引用

页数：17

共 8 条

[1] Genus 2 point counting over prime fields [J].