$G$-gerbes on perfectoid spaces
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917441481736192 |
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| author | Long, Xiaohuan Wang, Yibin Wu, Xiangdong Yi, Ru |
| author_facet | Long, Xiaohuan Wang, Yibin Wu, Xiangdong Yi, Ru |
| contents | Let $K$ be a complete non-archimedean field over $\mathbb{Q}_p$, $G$ be a rigid group over $K$, and $X$ be a perfectoid space over $K$. We consider the natural morphism of sites $ν: X_v \to X_{\mathrm{\acute{e}t}}$. It is known from work of Heuer that the direct image functor $ν_*$ induces an equivalence of the categories of $G$-torsors. In this article, we show that there is an equivalence of 2-categories of $G$-gerbes on these two topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $G$-gerbes on perfectoid spaces Long, Xiaohuan Wang, Yibin Wu, Xiangdong Yi, Ru Algebraic Geometry 14G45, 14F20, 14G22 Let $K$ be a complete non-archimedean field over $\mathbb{Q}_p$, $G$ be a rigid group over $K$, and $X$ be a perfectoid space over $K$. We consider the natural morphism of sites $ν: X_v \to X_{\mathrm{\acute{e}t}}$. It is known from work of Heuer that the direct image functor $ν_*$ induces an equivalence of the categories of $G$-torsors. In this article, we show that there is an equivalence of 2-categories of $G$-gerbes on these two topologies. |
| title | $G$-gerbes on perfectoid spaces |
| topic | Algebraic Geometry 14G45, 14F20, 14G22 |
| url | https://arxiv.org/abs/2511.15126 |