On orders in number fields: Picard groups, ring class fields and applications

doi:10.1007/s11425-015-4979-3

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	On orders in number fields: Picard groups, ring class fields and applications
	Lv Chang; Deng YingPu
	2015-08-01
Source Publication	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
Volume	58 Issue:8 Pages:1627-1638
Abstract	We focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group. As an application, we give criteria of the integral solvability of the diophantine equation p = x (2) + ny (2) over a class of imaginary quadratic fields where p is a prime element.
Keyword	orders Picard groups ring class fields integral points
DOI	10.1007/s11425-015-4979-3
Language	英语
Funding Project	National Natural Science Foundation of China[11471314] ; National Basic Research Program of China (973 Project)[2011CB302401] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000358172300004
Publisher	SCIENCE PRESS
Citation statistics	Cited Times:4[WOS] [WOS Record] [Related Records in WOS]
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/20413
Collection	系统科学研究所
Affiliation	Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
Recommended Citation GB/T 7714	Lv Chang,Deng YingPu. On orders in number fields: Picard groups, ring class fields and applications[J]. SCIENCE CHINA-MATHEMATICS,2015,58(8):1627-1638.
APA	Lv Chang,&Deng YingPu.(2015).On orders in number fields: Picard groups, ring class fields and applications.SCIENCE CHINA-MATHEMATICS,58(8),1627-1638.
MLA	Lv Chang,et al."On orders in number fields: Picard groups, ring class fields and applications".SCIENCE CHINA-MATHEMATICS 58.8(2015):1627-1638.

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