Finite Length for Unramified GL₂: Beyond Multiplicity One

2025/05/26 by Lucrezia Bertoletti, Bertoletti, Lucrezia
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.20134

openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number and K a finite unramified extension of ℚ_p. Building on recent work of Breuil, Herzig, Hu, Morra and Schraen, we study the smooth mod p representations of GL₂(K) appearing in a tower of mod p Hecke eigenspaces of the cohomology of Shimura curves, under mild genericity assumptions but notably no multiplicity one assumption at tame level, and prove that these representations are of finite length, thereby extending a previous result of the aforementioned authors.

Related

• Finite length for unramified GL₂: beyond multiplicity one, non-semisimple case
• Finite length for unramified GL₂
• On the constituents of the mod p cohomology of Shimura curves
• An application of a theorem of Emerton to mod p representations of GL₂
• Multiplicity one for the mod p cohomology of Shimura curves: the tame case