Finite Length for Unramified $GL_2$: Beyond Multiplicity One
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916759862247424 |
|---|---|
| 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 |