Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms

doi:10.1112/S0010437X0800376X

CSpace

	Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms
	Colliot-Thelene, Jean-Louis 1; Xu, Fei 2
	2009-03-01
发表期刊	COMPOSITIO MATHEMATICA
ISSN	0010-437X
卷号	145 期号:2 页码:309-363
摘要	An integer may be represented by a quadratic form over each ring of p-adic integers and over the reals without being represented by this quadratic form over the integers. More generally, such failure of a local-global principle may occur for the representation of one integral quadratic form by another integral quadratic form. We show that many such examples may be accounted for by a Brauer-Manin obstruction for the existence of integral points on schemes defined over the integers. For several types of homogeneous spaces of linear algebraic groups, this obstruction is shown to be the only obstruction to the existence of integral points.
关键词	integral quadratic forms integral points Hasse principle Brauer-Manin obstruction spinor exceptions homogeneous spaces of linear algebraic groups Galois colloniology
DOI	10.1112/S0010437X0800376X
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000265992800003
出版者	LONDON MATH SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7937
专题	中国科学院数学与系统科学研究院
通讯作者	Colliot-Thelene, Jean-Louis
作者单位	1.Univ Paris 11, CNRS, UMR 8628, F-91405 Orsay, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Colliot-Thelene, Jean-Louis,Xu, Fei. Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms[J]. COMPOSITIO MATHEMATICA,2009,145(2):309-363.
APA	Colliot-Thelene, Jean-Louis,&Xu, Fei.(2009).Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms.COMPOSITIO MATHEMATICA,145(2),309-363.
MLA	Colliot-Thelene, Jean-Louis,et al."Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms".COMPOSITIO MATHEMATICA 145.2(2009):309-363.