论文标题
对高纤维曲线的雅各布人的Weil多项式的限制
Restrictions on Weil polynomials of Jacobians of hyperelliptic curves
论文作者
论文摘要
受实验数据的启发，本文研究了在有限特征的有限特征领域定义的同等类的阿贝尔品种类别，其中包含过ellippiriptic曲线的雅各布式。我们通过证明过度椭圆形雅各比式的Weil多项式必须具有特定的形式模型2。对于固定的$ {g \ geq1} $，$ g $ g $ dimensional abelian品种的比例定义在$ \ \ \ \ nathbb {f} _q $ $ $ 1 $ 1-2（2^2） $ q \ to \ infty $范围在奇数pripe powers上，其中$ q（n）$表示$ n $的分区数量中的零件。
Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that the Weil polynomial of a hyperelliptic Jacobian must have a particular form modulo 2. For fixed ${g\geq1}$, the proportion of isogeny classes of $g$ dimensional abelian varieties defined over $\mathbb{F}_q$ which fail this condition is $1 - Q(2g + 2)/2^g$ as $q\to\infty$ ranges over odd prime powers, where $Q(n)$ denotes the number of partitions of $n$ into odd parts.
