On the generic part of the cohomology of compact unitary Shimura varieties

• 成果类型: Article
• 署名作者: Caraiani, Ana; Scholze, Peter
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.3.1
• 发表日期: 2017
• 页码: 649-766
• 关键词: galois representations; coefficients

摘要

The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the Hecke algebra satisfying a suitable genericity assumption. Along the way, we establish various foundational results on the geometry of the Hodge-Tate period map. In particular, we compare the fibres of the Hodge-Tate period map with Igusa varieties.