南方科技大学知识苑(SUSTech KC): PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES

题名	PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES
作者	Guo, Ning 1; Liu, Fei2
通讯作者	Guo, Ning
发表日期	2024
DOI	10.5802/jep.253
发表期刊	JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES 影响因子和分区
ISSN	2429-7100
EISSN	2270-518X
卷号	11
摘要	We establish an analogue of the Zariski-Nagata purity theorem for finite etale covers on smooth schemes over Prufer rings by demonstrating Auslander's flatness criterion in this non-Noetherian context. We derive an Auslander-Buchsbaum formula for general local rings, which provides a useful tool for studying the algebraic structures involved in our work. Through the analysis of reflexive sheaves, we prove various purity theorems for torsors under certain group algebraic spaces, such as the reductive ones. Specifically, using results from [EGA IV4] on parafactoriality on smooth schemes over normal bases, we prove the purity for cohomology groups of multiplicative type groups at this level of generality. Subsequently, we leverage the aforementioned purity results to resolve the Grothendieck-Serre conjecture for torsors under a quasi -split reductive group scheme over schemes smooth over Prufer rings. Along the way, we also prove a version of the Nisnevich purity conjecture for quasi -split reductive group schemes in our Pruferian context, inspired by the recent work of Cesnavi & ccaron;ius [Ces22b].
关键词	. Purity Zariski-Nagata Auslander-Buchsbaum Grothendieck-Serre vector bundles principal bundles Prufer rings torsors homogeneous spaces group schemes valuation rings
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	其他
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:001154779900001
出版者	ECOLE POLYTECHNIQUE
来源库	Web of Science
引用统计
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/789334
专题	理学院_数学系
作者单位	1.VA Steklov Math Inst, St Petersburg Branch, Fontanka 27, St Petersburg 191023, Russia 2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
推荐引用方式 GB/T 7714	Guo, Ning,Liu, Fei. PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES[J]. JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES,2024,11.
APA	Guo, Ning,&Liu, Fei.(2024).PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES.JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES,11.
MLA	Guo, Ning,et al."PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES".JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES 11(2024).