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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2502.13468 |
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| _version_ | 1866929720041406464 |
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| author | Shen, Xu Zhao, Ruishen |
| author_facet | Shen, Xu Zhao, Ruishen |
| contents | Let $G$ be a connected reductive group over a $p$-adic local field $F$. Rémy-Thuillier-Werner constructed embeddings of the (reduced) Bruhat-Tits building $\mathcal{B}(G,F)$ into the Berkovich spaces associated to suitable flag varieties of $G$, generalizing the work of Berkovich in split case. They defined compactifications of $\mathcal{B}(G,F)$ by taking closure inside these Berkovich flag varieties. We show that, in the setting of a basic local Shimura datum, the Rémy-Thuillier-Werner embedding factors through the associated $p$-adic Hodge-Tate period domain. Moreover, we compare the boundaries of the Berkovich compactification of $\mathcal{B}(G,F)$ with non basic Newton strata. In the case of $\mathrm{GL}_n$ and the cocharacter $μ=(1^d, 0^{n-d})$ for an integer $d$ which is coprime to $n$, we further construct a continuous retraction map from the $p$-adic period domain to the building. This reveals new information on these $p$-adic period domains, which share many similarities with the Drinfeld spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bruhat-Tits buildings and $p$-adic period domains Shen, Xu Zhao, Ruishen Number Theory Algebraic Geometry 11E95, 14G22 Let $G$ be a connected reductive group over a $p$-adic local field $F$. Rémy-Thuillier-Werner constructed embeddings of the (reduced) Bruhat-Tits building $\mathcal{B}(G,F)$ into the Berkovich spaces associated to suitable flag varieties of $G$, generalizing the work of Berkovich in split case. They defined compactifications of $\mathcal{B}(G,F)$ by taking closure inside these Berkovich flag varieties. We show that, in the setting of a basic local Shimura datum, the Rémy-Thuillier-Werner embedding factors through the associated $p$-adic Hodge-Tate period domain. Moreover, we compare the boundaries of the Berkovich compactification of $\mathcal{B}(G,F)$ with non basic Newton strata. In the case of $\mathrm{GL}_n$ and the cocharacter $μ=(1^d, 0^{n-d})$ for an integer $d$ which is coprime to $n$, we further construct a continuous retraction map from the $p$-adic period domain to the building. This reveals new information on these $p$-adic period domains, which share many similarities with the Drinfeld spaces. |
| title | Bruhat-Tits buildings and $p$-adic period domains |
| topic | Number Theory Algebraic Geometry 11E95, 14G22 |
| url | https://arxiv.org/abs/2502.13468 |