Compatibility of canonical l-adic local systems on adjoint Shimura varieties

• 成果类型: Article
• 署名作者: Klevdal, Christian; Patrikis, Stefan
• 署名单位: University of California System; University of California San Diego; University System of Ohio; Ohio State University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01357-6
• 发表日期: 2025
• 页码: 305-335
• 关键词: representations; points

摘要

For a Shimura variety (G,X) in the superrigid regime and neat level subgroup K0, we show that the canonical family of l-adic representations associated to a number field point y is an element of ShK0(G,X)(F), {rho y,l:Gal(Q/F)-> Gad(Ql)}l, form a compatible system of Gad(Ql)-representations: there is an integer N(y) such that for all l, rho y,l is unramified away from N(y)l, and for all l not equal l ' and v inverted iota N(y)ll ', the semisimple parts of the conjugacy classes of rho y,l(Frobv) and rho y,l '(Frobv) are (& Qopf;-rational and) equal. We deduce this from a stronger compatibility result for the canonical G(Ql)-valued local systems on connected Shimura varieties inside ShK0(G,X). Our theorems apply in particular to Shimura varieties of non-abelian type and represent the first such independence-of-l results in non-abelian type.