论文标题
计算一些具有较大还原稳定剂的均质品种上的积分点
Counting integral points on some homogeneous varieties with large reductive stabilizers
论文作者
论文摘要
令G为有理数的半圣像组，H是一个亚组，而不是有理数。给定稳定剂等于H的G和积分向量X的表示。在本文中，我们研究了具有有界高度的GX上积分点的渐近点。当h在G中h较大时，我们发现其渐近变量达到隐式常数，但我们允许存在中间亚组。这是通过在两个不同的设置中的两种等均分配的新组合来实现的：一种是在谎言组模块上的eSkin，mozes和shah的晶格，另一个是室内loir和tschinkel在平滑的投射品种上的结果，具有正常的交叉分裂。
Let G be a semisimple group over rational numbers and H is a subgroup over rational numbers. Given a representation of G and an integral vector x whose stabilizer is equal to H. In this paper we investigate the asymptotic of integral points on Gx with bounded height. We find its asymptotic up to an implicit constant when H is large in G but we allow the presence of intermediate subgroups. This is achieved by a novel combination of two equidistribution results in two different settings: one is that of Eskin, Mozes and Shah on a Lie group modulo a lattice and the other one is a result of Chamber-Loir and Tschinkel on a smooth projective variety with a normal crossing divisor.
