Brauer-Manin obstruction for Markoff surfaces

	Brauer-Manin obstruction for Markoff surfaces
	Colliot-Thelene, Jean-Louis 3; Wei, Dasheng 1,2; Xu, Fei 4
刊名	ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE
	2020
卷号	21 页码:1257-1313
ISSN号	0391-173X
英文摘要	Ghosh and Sarnak have studied integral points on surfaces defined by an equation x(2) + y(2) + z(2) - xyz = m over the integers. For these affine surfaces, we systematically study the Brauer group and the Brauer-Manin obstruction to the integral Hasse principle. We prove that strong approximation for integral points on any such surface, away from any finite set of places, fails, and that, for m not equal 0, 4, the Brauer group does not control strong approximation.
资助项目	National Natural Science Foundation of China[11622111]
WOS研究方向	Mathematics
语种	英语
出版者	SCUOLA NORMALE SUPERIORE
WOS记录号	WOS:000612618500037
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58085]
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.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France 4.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
推荐引用方式 GB/T 7714	Colliot-Thelene, Jean-Louis,Wei, Dasheng,Xu, Fei. Brauer-Manin obstruction for Markoff surfaces[J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE,2020,21:1257-1313.
APA	Colliot-Thelene, Jean-Louis,Wei, Dasheng,&Xu, Fei.(2020).Brauer-Manin obstruction for Markoff surfaces.ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE,21,1257-1313.
MLA	Colliot-Thelene, Jean-Louis,et al."Brauer-Manin obstruction for Markoff surfaces".ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE 21(2020):1257-1313.