论文标题
关于有限磁场的单力组的轨道枚举
On the enumeration of orbits of unipotent groups over finite fields
论文作者
论文摘要
我们表明，$ \ mathbf {z} $的线性轨道和共轭类的枚举在有限字段上定义的单一组定义的单一组在以下意义上是“野生”的：给定$ \ mathbf {z} $ y的任意方案$ y $ y $ y $ y $ \ bmod q^n $可以按照$ q $均匀地表示，就有限的许多$ \ mathbf {z} $的线性轨道数（或配偶类的数量）而言，$ \ \ \ \ \ \ mathbf {f} f} _q $ and laurent polynomials $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q $ q。
We show that the enumeration of linear orbits and conjugacy classes of $\mathbf{Z}$-defined unipotent groups over finite fields is "wild" in the following sense: given an arbitrary scheme $Y$ of finite type over $\mathbf{Z}$ and integer $n\geqslant 1$, the numbers $\# Y(\mathbf{F}_q) \bmod q^n$ can be expressed, uniformly in $q$, in terms of the numbers of linear orbits (or numbers of conjugacy classes) of finitely many $\mathbf{Z}$-defined unipotent groups over $\mathbf{F}_q$ and finitely many Laurent polynomials in $q$.
