Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: McDonald, Vaughan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416380707
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