On Some Generalized Rapoport-Zink Spaces

doi:10.4153/S0008414X19000269

CSpace

	On Some Generalized Rapoport-Zink Spaces
	Shen, Xu
	2020-10-01
发表期刊	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN	0008-414X
卷号	72 期号:5 页码:1111-1187
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.
关键词	Rapoport-Zink space shtuka Shimura variety K3 surface
DOI	10.4153/S0008414X19000269
收录类别	SCI
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000571654100001
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52209
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.