Transitivity of the $\mathbb{B}^+_\mathrm{dR}$-loop group action on Schubert cells
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908814743175168 |
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| author | Howe, Sean |
| author_facet | Howe, Sean |
| contents | For $G$ a connected linear algebraic group over a $p$-adic field, we show that the action of $G(\mathbb{B}^+_{\mathrm{dR}})$ on each Schubert cell in the $\mathbb{B}_{\mathrm{dR}}^+$-affine Grassmannian is transitive in the étale topology on affinoid perfectoids, generalizing a result in the reductive case due to Fargues and Scholze. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01204 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transitivity of the $\mathbb{B}^+_\mathrm{dR}$-loop group action on Schubert cells Howe, Sean Algebraic Geometry Number Theory For $G$ a connected linear algebraic group over a $p$-adic field, we show that the action of $G(\mathbb{B}^+_{\mathrm{dR}})$ on each Schubert cell in the $\mathbb{B}_{\mathrm{dR}}^+$-affine Grassmannian is transitive in the étale topology on affinoid perfectoids, generalizing a result in the reductive case due to Fargues and Scholze. |
| title | Transitivity of the $\mathbb{B}^+_\mathrm{dR}$-loop group action on Schubert cells |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2505.01204 |