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Main Author: Bertoletti, Lucrezia
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.20134
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author Bertoletti, Lucrezia
author_facet Bertoletti, Lucrezia
contents Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Building on recent work of Breuil, Herzig, Hu, Morra and Schraen, we study the smooth mod $p$ representations of $\mathrm{GL}_2(K)$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_20134
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Finite Length for Unramified $GL_2$: Beyond Multiplicity One
Bertoletti, Lucrezia
Number Theory
Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Building on recent work of Breuil, Herzig, Hu, Morra and Schraen, we study the smooth mod $p$ representations of $\mathrm{GL}_2(K)$ 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.
title Finite Length for Unramified $GL_2$: Beyond Multiplicity One
topic Number Theory
url https://arxiv.org/abs/2505.20134