A Galois side analogue of a theorem of Bernstein

2015/07/04 by Manish Mishra, Mishra, Manish
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Polynomial and algebraic computation #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1507.01078

To appear in JRMS

arxiv created 2015/07/04 · openalex publication_date 2015/07/04 · arxiv updated 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive group defined over a non archimedean local field k. A theorem of Bernstein states that for any compact open subgroup K of G(k), there are, up to unramified twists, only finitely many K-spherical supercuspidal representations of G(k). We prove an analogous result on the Galois side of the Langlands correspondence.

Related

• Regular Bernstein blocks
• Progrès récents sur les représentations supercuspidales
• Globalization of supercuspidal representations over function fields and\n applications
• Supercuspidal L-packets
• The Explicit Local Langlands Correspondence for G₂