Reduction mod $p$ of semi-stable representations of some super-Breuil weights
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910143272189952 |
|---|---|
| author | Chitrao, Anand Ghate, Eknath |
| author_facet | Chitrao, Anand Ghate, Eknath |
| contents | We determine the mod $p$ reductions of the semi-stable representations $V_{k, \mathcal{L}}$ of weight $k \in [p + 5, 2p]\cup[2p + 6, 3p + 1]$ and $v_p(\mathcal{L}) < 1-k/2$ for primes $p \geq 5$. In particular, this shows that the techniques introduced in [CG24] involving the $p$-adic and mod $p$ local Langlands correspondences can be used to compute the reduction of $V_{k, \mathcal{L}}$ outside the range $k \in [3, p + 1]$. Moreover, this shows that the bound on $v_p(\mathcal{L})$ given by Bergdall-Levin-Liu [BLL23] can be improved, at least for weights $k \in [2p + 6, 3p + 1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reduction mod $p$ of semi-stable representations of some super-Breuil weights Chitrao, Anand Ghate, Eknath Number Theory 11F80 We determine the mod $p$ reductions of the semi-stable representations $V_{k, \mathcal{L}}$ of weight $k \in [p + 5, 2p]\cup[2p + 6, 3p + 1]$ and $v_p(\mathcal{L}) < 1-k/2$ for primes $p \geq 5$. In particular, this shows that the techniques introduced in [CG24] involving the $p$-adic and mod $p$ local Langlands correspondences can be used to compute the reduction of $V_{k, \mathcal{L}}$ outside the range $k \in [3, p + 1]$. Moreover, this shows that the bound on $v_p(\mathcal{L})$ given by Bergdall-Levin-Liu [BLL23] can be improved, at least for weights $k \in [2p + 6, 3p + 1]$. |
| title | Reduction mod $p$ of semi-stable representations of some super-Breuil weights |
| topic | Number Theory 11F80 |
| url | https://arxiv.org/abs/2604.16867 |