Geometric translations of $(φ,Γ)$-modules for $\mathrm{GL}_2(\mathbb{Q}_p)$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909798855868416 |
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| author | Wu, Zhixiang |
| author_facet | Wu, Zhixiang |
| contents | We study ``change of weights'' maps between loci of the stack of $(φ,Γ)$-modules over the Robba ring with integral Hodge-Tate-Sen weights. We show that in the $\mathrm{GL}_2(\mathbb{Q}_p)$ case these maps can realize translations of $(φ,Γ)$-modules geometrically. The motivation is to investigate translations of locally analytic representations under the categorical $p$-adic Langlands correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric translations of $(φ,Γ)$-modules for $\mathrm{GL}_2(\mathbb{Q}_p)$ Wu, Zhixiang Number Theory Representation Theory We study ``change of weights'' maps between loci of the stack of $(φ,Γ)$-modules over the Robba ring with integral Hodge-Tate-Sen weights. We show that in the $\mathrm{GL}_2(\mathbb{Q}_p)$ case these maps can realize translations of $(φ,Γ)$-modules geometrically. The motivation is to investigate translations of locally analytic representations under the categorical $p$-adic Langlands correspondence. |
| title | Geometric translations of $(φ,Γ)$-modules for $\mathrm{GL}_2(\mathbb{Q}_p)$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2405.16637 |