Global rigid inner forms and multiplicities of discrete automorphic representations

2015/01/07 by Kaletha, Tasho · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1501.01667

Abstract

Given a number field we construct a canonical Galois gerbe over it and show that its cohomology provides a bridge between the refined local endoscopy introduced in arXiv:1304.3292 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 construction 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.

Cited by

• Component groups for non-supercuspidal L-parameters for p-adic SL₃

Related

• Rigid inner forms over global function fields
• Global rigid inner forms vs isocrystals
• Rigid inner forms of real and p-adic groups
• Arthur packets for metaplectic groups
• Strong local-global phenomena for Galois and automorphic representations