On Some Generalized Rapoport-Zink Spaces
文献类型：期刊论文
| 作者 | Shen, Xu |
| 刊名 | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
 |
| 出版日期 | 2020-10-01 |
| 卷号 | 72期号:5页码:1111-1187 |
| 关键词 | Rapoport-Zink space shtuka Shimura variety K3 surface |
| ISSN号 | 0008-414X |
| DOI | 10.4153/S0008414X19000269 |
| 英文摘要 | We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated p-adic reductive groups. Such obtained Rapoport-Zink spaces are said to be of abelian type. The class of Rapoport-Zink spaces of abelian type is strictly larger than the class of Rapoport-Zink spaces of Hodge type, but the two type spaces are closely related as having isomorphic connected components. The rigid analytic generic fibers of Rapoport-Zink spaces of abelian type can be viewed as moduli spaces of local G-shtukas in mixed characteristic in the sense of Scholze. We prove that Shimura varieties of abelian type can be uniformized by the associated Rapoport-Zink spaces of abelian type. We construct and study the Ekedahl-Oort stratifications for the special fibers of Rapoport-Zink spaces of abelian type. As an application, we deduce a Rapoport-Zink type uniformization for the supersingular locus of the moduli space of polarized K3 surfaces in mixed characteristic. Moreover, we show that the Artin invariants of supersingular K3 surfaces are related to some purely local invariants. |
| 资助项目 | Chinese Academy of Sciences[50Y64198900] ; Chinese Academy of Sciences[29Y64200900] ; Recruitment Program of Global Experts of China ; NSFC[11631009] ; NSFC[11688101] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000571654100001 |
| 出版者 | CAMBRIDGE UNIV PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52208]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Shen, Xu |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Shen, Xu. On Some Generalized Rapoport-Zink Spaces[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2020,72(5):1111-1187. |
| APA | Shen, Xu.(2020).On Some Generalized Rapoport-Zink Spaces.CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,72(5),1111-1187. |
| MLA | Shen, Xu."On Some Generalized Rapoport-Zink Spaces".CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 72.5(2020):1111-1187. |
入库方式： OAI收割
来源：数学与系统科学研究院
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