Two-torsion in the Jacobian of hyperelliptic curves over finite fields
Two-torsion in the Jacobian of hyperelliptic curves over finite fields
复制标题
有限域上超椭圆曲线雅可比行列式的二阶扭转
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
G. Cornelissen
中科院分区：
文献类型：
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作者：
G. Cornelissen
抽象。我们确定$$ {f{F}}_2 $$-向量空间$$ {环上超椭圆曲线Jacobian中的f{F}}_q $$-有理2-扭点f{F}} q $（q奇）的判别式的有理因子的阶，并将其与相应函数域的亏格理论联系起来.作为推论，我们证明了某些真实的超椭圆曲线的雅可比矩阵中存在一个> 2阶点。
Abstract. We determine the exact dimension of the $$ {f{F}}_2 $$-vector space of $$ {f{F}}_q $$-rational 2-torsion points in the Jacobian of a hyperelliptic curve over $$ {f{F}}_q $$ (q odd) in terms of the degrees of the rational factors of its discriminant, and relate this to genus theory for the corresponding function field. As a corollary, we prove the existence of a point of order > 2 in the Jacobian of certain real hyperelliptic curves.