Moduli stacks of Galois representations and the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908415010275328 |
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| author | Johansson, Christian Newton, James Wang-Erickson, Carl |
| author_facet | Johansson, Christian Newton, James Wang-Erickson, Carl |
| contents | We give a categorical formulation of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$,as an embedding of the derived category of locally admissible representations into the category of Ind-coherent sheaves on the moduli stack of two-dimensional representations of $\mathrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$. Moreover, we relate our version of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$ to the cohomology of modular curves through a local-global compatibility formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moduli stacks of Galois representations and the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$ Johansson, Christian Newton, James Wang-Erickson, Carl Number Theory Representation Theory We give a categorical formulation of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$,as an embedding of the derived category of locally admissible representations into the category of Ind-coherent sheaves on the moduli stack of two-dimensional representations of $\mathrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$. Moreover, we relate our version of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$ to the cohomology of modular curves through a local-global compatibility formula. |
| title | Moduli stacks of Galois representations and the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbb{Q}_p)$ |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2403.19565 |