Rigid inner forms of real and p-adic groups

2013/04/11 by Tasho Kaletha, Kaletha, Tasho · 6 citations
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1304.3292

58 pages. v5: Changes to introduction, exposition, and notation

arxiv created 2015/02/09 · arxiv updated 2015/02/10

Abstract

We define a new cohomology set for an affine algebraic group G and a multiplicative finite central subgroup Z, both defined over a local field of characteristic zero, which is an enlargement of the usual first Galois cohomology set of G. We show how this set can be used to normalize the Langlands-Shelstad endoscopic transfer factors and to give a conjectural description of the internal structure and endoscopic transfer of L-packets for arbitrary connected reductive groups that extends the well-known conjectural description for quasi-split groups. In the real case, we show that this description is correct using Shelstad's work.

Cited by

• Parameters and Theta lifts
• The local Langlands conjecture
• The FPP Conjecture for p-adic Groups
• Depth Preservation and Close-Field Transfer in the Local Langlands Correspondence
• Rigid inner forms vs isocrystals
• Global rigid inner forms and multiplicities of discrete automorphic representations

Related

• Rigid inner forms over global function fields
• Global rigid inner forms and multiplicities of discrete automorphic representations
• Rigid inner forms vs isocrystals
• Non-basic rigid packets for discrete L-parameters
• Transfer of R-groups between p-adic inner forms of SL_n