Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2504.09270 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917984137641984 |
|---|---|
| author | Wang, Yitong |
| author_facet | Wang, Yitong |
| contents | Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Let $π$ be an admissible smooth mod $p$ representation of $\mathrm{GL}_2(K)$ occurring in some Hecke eigenspaces of the mod $p$ cohomology and $\overline{r}$ be its underlying global two-dimensional Galois representation. When $\overline{r}$ satisfies some Taylor-Wiles hypotheses and is sufficiently generic at $p$, we compute explicitly certain constants appearing in the diagram associated to $π$, generalizing the results of Dotto-Le. As a result, we prove that the associated étale $(φ,\mathcal{O}_K^{\times})$-module $D_A(π)$ defined by Breuil-Herzig-Hu-Morra-Schraen is explicitly determined by the restriction of $\overline{r}$ to the decomposition group at $p$, generalizing the results of Breuil-Herzig-Hu-Morra-Schraen and the author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diamond diagrams and multivariable $(φ,\mathcal{O}_K^{\times})$-modules Wang, Yitong Number Theory Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Let $π$ be an admissible smooth mod $p$ representation of $\mathrm{GL}_2(K)$ occurring in some Hecke eigenspaces of the mod $p$ cohomology and $\overline{r}$ be its underlying global two-dimensional Galois representation. When $\overline{r}$ satisfies some Taylor-Wiles hypotheses and is sufficiently generic at $p$, we compute explicitly certain constants appearing in the diagram associated to $π$, generalizing the results of Dotto-Le. As a result, we prove that the associated étale $(φ,\mathcal{O}_K^{\times})$-module $D_A(π)$ defined by Breuil-Herzig-Hu-Morra-Schraen is explicitly determined by the restriction of $\overline{r}$ to the decomposition group at $p$, generalizing the results of Breuil-Herzig-Hu-Morra-Schraen and the author. |
| title | Diamond diagrams and multivariable $(φ,\mathcal{O}_K^{\times})$-modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.09270 |