Banach-Hecke algebras and p-adic Galois Representations

2005/10/30 by Peter Schneider, Schneider, Peter, Jeremy Teitelbaum +1
Mathematics · #11S37 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories #math.NT #math.RT #msc:11S37 #msc:22E50

paper · pdf · doi:10.48550/arxiv.math/0510661

Dedicated to John Coates on his 60th birthday

arxiv created 2005/10/30 · openalex publication_date 2005/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We take some initial steps towards illuminating the (hypothetical) p-adic local Langlands functoriality principle relating Galois representations of a p-adic field L and admissible unitary Banach space representations of G(L) when G is a split reductive group over L. The outline of our work is derived from Breuil's remarkable insights into the nature of the correspondence between 2-dimensional crystalline Galois representations of the Galois group of \Qdss_p and Banach space representations of GL₂(\Qdss_p).

Related

• First steps towards p-adic Langlands functoriality
• The p-adic local Langlands correspondence for GL₂(Q_p)
• p-adic Banach space representations of SL₂(\mathbb Q_p)
• The semi-stable Local Langlands Correspondence
• Strong local-global compatibility in the p-adic Langlands program for U(2)