Connected components of the moduli space of L-parameters

2024/04/25 by Sean Cotner, Cotner, Sean
Mathematics · #11F80 #20G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2404.16716

openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, in order to formulate a categorical version of the local Langlands correspondence, several authors have constructed moduli spaces of Z[1/p]-valued L-parameters for p-adic groups. The connected components of these spaces over various Z[1/p]-algebras R are conjecturally related to blocks in categories of R-representations of p-adic groups. Dat-Helm-Kurinczuk-Moss described the components when R is an algebraically closed field and gave a conjectural description when R = Z[1/p]. In this paper, we prove a strong form of this conjecture applicable to any integral domain R over Z[1/p].

Related

• Moduli of Langlands Parameters
• The semi-stable Local Langlands Correspondence
• Local Langlands in families: The banal case
• Moduli stacks of Galois representations and the p-adic local Langlands correspondence for GL₂(ℚ_p)
• On multiplicity in restriction of tempered representations of p-adic\n groups