Local Jacquet - Langlands correspondence and congruence modulo

• 成果类型: Article
• 署名作者: Minguez, Alberto; Secherre, Vincent
• 署名单位: Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0696-y
• 发表日期: 2017
• 页码: 553-631
• 关键词: general linear-groups; irreducible representations; smooth representations; inner forms; gl(m) d; gl(n); DECOMPOSITION; field

摘要

Let be a non-Archimedean local field of residual characteristic p, and be a prime number different from p. We consider the local Jacquet-Langlands correspondence between -adic discrete series of and an inner form . We show that it respects the relationship of congruence modulo . More precisely, we show that two integral -adic discrete series of are congruent modulo if and only if the same holds for their Jacquet-Langlands transfers to . We also prove that the Langlands-Jacquet morphism from the Grothendieck group of finite length -adic representations of to that of defined by Badulescu is compatible with reduction mod l.