论文标题
$ a $ number，$ p $ -rank和Cartier of属属4曲线
The $a$-number, $p$-rank and Cartier points of genus 4 curves
论文作者
论文摘要
我们研究了有限田地的$ 4 $曲线，以及$ p $ torsion的两个不变部分的jacobians：$ a $ number（$ a $）和$ p $ -rank（$ f $）。我们收集和分析曲线的统计数据，超过$ \ mathbb {f} _p $ for $ p = 3,5,7,11 $及其不变性。然后，我们研究了卡地亚点的存在，这也与$ j [p] $的结构有关。对于$ 0 \ leq a <g $的曲线，卡地亚点的数量是有限的，并且取决于$ a $ a和$ f $。
We study genus $4$ curves over finite fields and two invariants of the $p$-torsion part of their Jacobians: the $a$-number ($a$) and $p$-rank ($f$). We collect and analyze statistical data of curves over $\mathbb{F}_p$ for $p=3,5,7,11$ and their invariants. Then, we study the existence of Cartier points, which are also related to the structure of $J[p]$. For curves with $0\leq a<g$, the number of Cartier points is bounded, and it depends on $a$ and $f$.
