Rigid inner forms vs isocrystals

2015/02/02 by Kaletha, Tasho · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1502.00650

Abstract

We compare two statements of the refined local Langlands correspondence for connected reductive groups defined over a p-adic field -- one involving Kottwitz's set B(G) of isocrystals with additional structure, and one involving the cohomology set H¹(u -> W,Z -> G) introduced in arXiv:1304.3292. We show that if either statement is valid for all connected reductive groups, then so is the other. We also discuss how the second statement depends on the choice of element of H¹(u -> W,Z -> G).

Cited by

• The local Langlands conjecture

Related

• Isocrystals and limits of rigid local Langlands correspondences
• Rigid inner forms of real and p-adic groups
• Non-basic rigid packets for discrete L-parameters
• Depth Preservation and Close-Field Transfer in the Local Langlands Correspondence
• The B(G)-parametrization of the local Langlands correspondence