On a conjecture of Rapoport and Zink

• 成果类型: Article
• 署名作者: Hartl, Urs
• 署名单位: University of Munster
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0437-9
• 发表日期: 2013
• 页码: 627-696
• 关键词: algebraic extensions; hodge-structures; rigid geometry; period spaces; REPRESENTATIONS; crystalline; COHOMOLOGY; CONSTRUCTION; isocrystals

摘要

In their book, Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of p-divisible groups to some of these period spaces. They conjectured the existence of an ,tale bijective morphism of rigid analytic spaces and of a universal local system of ae (p) -vector spaces on . Such a local system would give rise to a tower of ,tale covering spaces of , equipped with a Hecke-action, and an action of the automorphism group J(ae (p) ) of the isocrystal with extra structure. For Hodge-Tate weights n-1 and n we construct in this article an intrinsic Berkovich open subspace of and the universal local system on . We show that only in exceptional cases equals all of and when the Shimura group is we determine all these cases. We conjecture that the rigid-analytic space associated with is the maximal possible , and that is connected. We give evidence for these conjectures. For those period spaces possessing PEL period morphisms, we show that equals the image of the period morphism. Then our local system is the rational Tate module of the universal p-divisible group and carries a J(ae (p) )-linearization. We construct the tower of ,tale covering spaces, and we show that it is canonically isomorphic in a Hecke and J(ae (p) )-equivariant way to the tower constructed by Rapoport and Zink using the universal p-divisible group.