Truncations of level 1 of elements in the loop group of a reductive group

• 成果类型: Article
• 署名作者: Viehmann, Eva
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.179.3.3
• 发表日期: 2014
• 页码: 1009-1040
• 关键词: ekedahl-oort strata; abelian-varieties; additional structure; newton strata; MODULI SPACES; stratification; CLASSIFICATION; isocrystals

摘要

The aim of this article is to define and study a new invariant of elements of loop groups that is invariant under sigma-conjugation by a hyperspecial maxi mal open subgroup and that we call the truncation of level 1. We classify truncations of level 1 and describe their specialization behavior. Further m ore, we prove group-theoretic conditions for the set of sigma-conjugacy classes obtained from elements of a given truncation of level 1 and in particular for the generic sigma-conjugacy class in any given truncation stratum. In the last section we relate our invariant to the Ekedahl-Oort stratification of the Siegel moduli space and to generalizations to other PEL Shimura varieties.