Title: Counting integral points on some homogeneous varieties with large reductive stabilizers Show Chinese title

Title: 在具有大约化稳定子的某些齐次流形上计数整数点

Abstract: 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. Show Chinese abstract

Abstract: 设G为有理数上的半单群，H为有理数上的子群。给定G的一个表示和一个积分向量x，其稳定子等于H。在本文中，我们研究了在有界高度下Gx上的积分点的渐进行为。当H在G中较大时，我们找到了其渐进行为，但允许存在中间子群。这是通过在两种不同设置中两个等分布结果的创新结合实现的：一个是Eskin、Mozes和Shah在模格的李群上的等分布结果，另一个是Chamber-Loir和Tschinkel在具有法相交除子的光滑射影流形上的结果。