Bessel F-isocrystals for reductive groups

• 成果类型: Article
• 署名作者: Xu, Daxin; Zhu, Xinwen
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; California Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01079-5
• 发表日期: 2022
• 页码: 997-1092
• 关键词: irregular connection; logarithmic growth; filtrations; COHOMOLOGY; THEOREM; REPRESENTATIONS; Duality; MODULES

摘要

We construct the Frobenius structure on a rigid connection Be (sic) on G(m) for a split reductive group (sic) introduced by Frenkel-Gross. These data form a (sic)-valued overconvergent F-isocrystal Be-(sic)(dagger) on G(m), F-p, which is the p-adic companion of the Kloosterman (sic)-local system Kl((sic)) constructed by Heinloth-Ngo-Yun. By studying the structure of the underlying differential equation, we calculate themonodromy group of Be-(sic)(dagger) when (sic) is almost simple (which recovers the calculation of monodromy group of Kl((sic)) due to Katz and Heinloth-Ngo-Yun), and prove a conjecture of Heinloth-Ngo-Yun on the functoriality between different Kloosterman (sic)-local systems. We show that the Frobenius Newton polygons of Kl(sic) are generically ordinary for every (sic) and are everywhere ordinary on vertical bar G(m), F-p vertical bar when (sic) is classical or G(2).