Arithmetic purity of strong approximation for homogeneous spaces

被引：10

作者：

Cao, Yang ^{[1
]}

Liang, Yongqi ^{[2
]}

Xu, Fei ^{[3
]}

机构：

[1] Max Planck Inst Math, Bonn, Germany

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[3] Capital Normal Univ, Sch Math Sci, 105 Xisanhuanbeilu, Beijing 100048, Peoples R China

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 132卷

关键词：

Strong approximation; Purity; Brauer-Manin obstruction; (Linear) algebraic groups; Bruhat decomposition; Homogeneous spaces; BRAUER-MANIN OBSTRUCTION; INTEGRAL POINTS; VARIETIES; FIELD;

D O I：

10.1016/j.matpur.2019.02.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that any open subset U of a semi-simple simply connected quasi-split linear algebraic group G with codim(G \ U, G) >= 2 over a number field satisfies strong approximation by establishing a fibration of G over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given. (C) 2019 Elsevier Masson SAS. All rights reserved.

引用

页码：334 / 368

页数：35

共 51 条

[1]

[Anonymous], 1980, PRINCETON MATH SERIE

[2]

[Anonymous], 2014, Math. Sci. Res. Inst. Publ

[3] Manin obstruction to strong approximation for homogeneous spaces [J].