Eigenvarieties over CM fields and trianguline representations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910918970966016 |
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| author | McDonald, Vaughan |
| author_facet | McDonald, Vaughan |
| contents | We show that the Galois representations associated to points on certain (derived) eigenvarieties for $\operatorname{GL}_n$ over a CM field are trianguline with the expected Sen weights, verifying an analogue of a conjecture of Hansen in many cases. The proof follows the strategy of passing to a larger unitary group $\widetilde{G}$ of signature $(n,n)$, where the key new input is an analytic continuation result for an eigenvariety for $\widetilde{G}$ localised at an Eisenstein maximal ideal. We also discuss the (subtle) relation of eigenvarieties for $\operatorname{GL}_n$ with the trianguline variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvarieties over CM fields and trianguline representations McDonald, Vaughan Number Theory We show that the Galois representations associated to points on certain (derived) eigenvarieties for $\operatorname{GL}_n$ over a CM field are trianguline with the expected Sen weights, verifying an analogue of a conjecture of Hansen in many cases. The proof follows the strategy of passing to a larger unitary group $\widetilde{G}$ of signature $(n,n)$, where the key new input is an analytic continuation result for an eigenvariety for $\widetilde{G}$ localised at an Eisenstein maximal ideal. We also discuss the (subtle) relation of eigenvarieties for $\operatorname{GL}_n$ with the trianguline variety. |
| title | Eigenvarieties over CM fields and trianguline representations |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.18319 |