Converse theorems and the local Langlands correspondence in families

• 成果类型: Article
• 署名作者: Helm, David; Moss, Gilbert
• 署名单位: Imperial College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0816-y
• 发表日期: 2018
• 页码: 999-1022
• 关键词: gl(n)

摘要

We prove a descent criterion for certain families of smooth representations of modules (the so-called integral Bernstein center) in terms of Galois theory and the local Langlands correspondence. An immediate consequence is the conjectural local Langlands correspondence in families of Emerton and Helm (Ann Sci Ec Norm Super (4) 47(4):655-722, 2014).