论文标题
$ t^{2g}+at^g+q^g $的Weil多项式的某些算术属性
Some arithmetic properties of Weil polynomials of the form $t^{2g}+at^g+q^g$
论文作者
论文摘要
如果$ \ Mathcal {a} $中的每个品种都有一个有理点的循环群，则据说在有限字段定义的ABELIAN品种的Abelian品种的$ \ Mathcal {A} $都被称为“环状”。在本文中，我们研究了阿伯利亚品种的威尔 - 中心同种阶层类别的局部循环性，即具有$ f_ \ mathcal {a}（t）= t^{2g}+at^g+q^g $的多项式的那些，以及在$ qutieties $ natione $ nath $ nath $ nath $ a $ n of varieties $ n $ n of varieties $ n $ n n $ n n $ n n $ n n $ n n $ {我们利用标准：使用Weil多项式$ f $的同类级$ \ Mathcal {a} $是循环的，并且仅当$ f'（1）$与$ f（1）$ coprime与$ f（1）$划分为自由基。
An isogeny class $\mathcal{A}$ of abelian varieties defined over finite fields is said to be "cyclic" if every variety in $\mathcal{A}$ has a cyclic group of rational points. In this paper we study the local cyclicity of Weil-central isogeny classes of abelian varieties, i.e. those with Weil polynomials of the form $f_\mathcal{A}(t)=t^{2g}+at^g+q^g$, as well as the local growth of the groups of rational points of the varieties in $\mathcal{A}$ after finite field extensions. We exploit the criterion: an isogeny class $\mathcal{A}$ with Weil polynomial $f$ is cyclic if and only if $f'(1)$ is coprime with $f(1)$ divided by its radical.
