Global rigid inner forms and multiplicities of discrete automorphic representations

• 成果类型: Article
• 署名作者: Kaletha, Tasho
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0791-3
• 发表日期: 2018
• 页码: 271-369
• 关键词: stable trace formula; isocrystals; series

摘要

We study the cohomology of certain Galois gerbes over number fields. This cohomology provides a bridge between refined local endoscopy, as introduced in Kaletha (Ann Math (2) 184(2):559-632, 2016), and classical global endoscopy. As particular applications, we express the canonical adelic transfer factor that governs the stabilization of the Arthur-Selberg trace formula as a product of normalized local transfer factors, we give an explicit constriction of the pairing between an adelic L-packet and the corresponding S-group (based on the conjectural pairings in the local setting) that is the essential ingredient in the description of the discrete automorphic spectrum of a reductive group, and we give a proof of some expectations of Arthur.