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

文献类型：期刊论文

作者Colliot-Thelene, Jean-Louis1; Xu, Fei2
刊名COMPOSITIO MATHEMATICA
出版日期2009-03-01
卷号145期号:2页码:309-363
关键词integral quadratic forms integral points Hasse principle Brauer-Manin obstruction spinor exceptions homogeneous spaces of linear algebraic groups Galois colloniology
ISSN号0010-437X
DOI10.1112/S0010437X0800376X
英文摘要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.
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000265992800003
出版者LONDON MATH SOC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/7936]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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