| 题名 | PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES |
| 作者 | |
| 通讯作者 | Guo, Ning |
| 发表日期 | 2024
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| DOI | |
| 发表期刊 | |
| ISSN | 2429-7100
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| EISSN | 2270-518X
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| 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 | |
| 相关链接 | [来源记录] |
| 收录类别 | |
| 语种 | 英语
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| 学校署名 | 其他
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| WOS研究方向 | Mathematics
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| WOS类目 | Mathematics
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| WOS记录号 | WOS:001154779900001
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| 出版者 | |
| 来源库 | Web of Science
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| 引用统计 | |
| 成果类型 | 期刊论文 |
| 条目标识符 | //www.snoollab.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.
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| APA |
Guo, Ning,&Liu, Fei.(2024).PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES.JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES,11.
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| MLA |
Guo, Ning,et al."PURITY AND QUASI-SPLIT TORSORS OVER PRÃ FER BASES".JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES 11(2024).
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| 条目包含的文件 | 条目无相关文件。 | |||||
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