论文标题
计数扭转点上的代数曲线
Counting torsion points on subvarieties of the algebraic torus
论文作者
论文摘要
我们估计功能的增长率，该功能计算了代数圆环$ \ mathbb g_m^n $在某些代数封闭的字段上的代数子变量上最多$ t $的扭转点。我们证明了一个锋利的一般上限，并表征了生长速率最大的亚体。对于所有其他亚地区，与一般性相比，有一个更好的界限，可以节省动力。我们的结果包括在特征性零中的渐近公式，我们使用laurent的定理，即曼宁·穆福德的猜想。但是，我们还获得了$ k $的新上限，即有限场的代数关闭。
We estimate the growth rate of the function which counts the number of torsion points of order at most $T$ on an algebraic subvariety of the algebraic torus $\mathbb G_m^n$ over some algebraically closed field. We prove a general upper bound which is sharp, and characterize the subvarieties for which the growth rate is maximal. For all other subvarieties there is a better bound which is power saving compared to the general one. Our result includes asymptotic formulas in characteristic zero where we use Laurent's Theorem, the Manin-Mumford Conjecture. However, we also obtain new upper bounds for $K$ the algebraic closure of a finite field.
