Top-dimensional rational cohomology of the congruence subgroup $Γ_{0,n}^+(p)$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918518304276480 |
|---|---|
| author | Abdelnaim, Tatiana |
| author_facet | Abdelnaim, Tatiana |
| contents | Let $Γ_{0,n}^+(p)\subset \mathrm{SL}_n(\mathbb{Z})$ be the congruence subgroup of level-$p$ whose first column is of the form $(*,0,\dots,0)^t\bmod p$. We prove that the top-dimensional cohomology group $H^{\binom{n}{2}}(Γ_{0,n}^+(p);\mathbb{Q})$ vanishes for $p\in\{2,3,5,7,13\}$ if $n \geq 3$, as well as for $p \leq 6n-14$.
Additionally, we prove a non-vanishing result, showing that this cohomology group is nonzero for $n = 2$ for every prime $p$, and for $n=3$ for all primes $p \notin \{2,3,5,7,13\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Top-dimensional rational cohomology of the congruence subgroup $Γ_{0,n}^+(p)$ Abdelnaim, Tatiana Algebraic Topology Number Theory 11F75, 55U10 Let $Γ_{0,n}^+(p)\subset \mathrm{SL}_n(\mathbb{Z})$ be the congruence subgroup of level-$p$ whose first column is of the form $(*,0,\dots,0)^t\bmod p$. We prove that the top-dimensional cohomology group $H^{\binom{n}{2}}(Γ_{0,n}^+(p);\mathbb{Q})$ vanishes for $p\in\{2,3,5,7,13\}$ if $n \geq 3$, as well as for $p \leq 6n-14$. Additionally, we prove a non-vanishing result, showing that this cohomology group is nonzero for $n = 2$ for every prime $p$, and for $n=3$ for all primes $p \notin \{2,3,5,7,13\}$. |
| title | Top-dimensional rational cohomology of the congruence subgroup $Γ_{0,n}^+(p)$ |
| topic | Algebraic Topology Number Theory 11F75, 55U10 |
| url | https://arxiv.org/abs/2605.23526 |