Non-admissibility of some universal supersingular representations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913138008391680 |
|---|---|
| author | Feng, Zachary Lee, Heejong Li, Ray McDonald, Vaughan Reddy, Nischay |
| author_facet | Feng, Zachary Lee, Heejong Li, Ray McDonald, Vaughan Reddy, Nischay |
| contents | Let $K/\mathbf{Q}_p$ be an unramified extension of degree $f$ with residue field $k$. Let $σ$ be an irreducible representation of $\mathrm{GL}_n(k)$ over $\overline{\mathbf{F}}_p$. For $n\ge 3$, we prove that the universal supersingular representation of weight $σ$ is non-admissible and of infinite length when $σ$ is sufficiently generic and satisfies certain technical conditions. This generalizes the previous results for $n=2$ and a non-trivial finite extension $K/\mathbf{Q}_p$. Our method employs a weight cycling argument together with recent progress on the Serre weight conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17836 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-admissibility of some universal supersingular representations Feng, Zachary Lee, Heejong Li, Ray McDonald, Vaughan Reddy, Nischay Number Theory Representation Theory Let $K/\mathbf{Q}_p$ be an unramified extension of degree $f$ with residue field $k$. Let $σ$ be an irreducible representation of $\mathrm{GL}_n(k)$ over $\overline{\mathbf{F}}_p$. For $n\ge 3$, we prove that the universal supersingular representation of weight $σ$ is non-admissible and of infinite length when $σ$ is sufficiently generic and satisfies certain technical conditions. This generalizes the previous results for $n=2$ and a non-trivial finite extension $K/\mathbf{Q}_p$. Our method employs a weight cycling argument together with recent progress on the Serre weight conjectures. |
| title | Non-admissibility of some universal supersingular representations |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2605.17836 |