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• W2809565904 abstract "Let F / Q be a CM field where p splits completely and r ¯ : Gal ( Q ¯ / F ) → GL 3 ( F ¯ p ) a continuous modular Galois representation. Assume that r ¯ is non-ordinary and non-split reducible (niveau 2) at a place w above p. We show that the isomorphism class of r ¯ | Gal ( F ¯ w / F w ) is determined by the GL 3 ( F w ) -action on the space of mod p algebraic automorphic forms using the refined Hecke action of Herzig, Le and Morra [Compos. Math. 153 (2017) 2215–2286]. We also give a nearly optimal weight elimination result for niveau 2 Galois representations compatible with the explicit conjectures of Gee, Herzig and Savitt [J. Eur. Math. Soc., to appear] and Herzig [Duke Math. J. 149 (2009) 37–116]. Moreover, we prove the modularity of certain Serre weights, in particular, when the Fontaine–Laffaille invariant takes special value ∞, our methods establish the modularity of a certain shadow weight." @default.
• W2809565904 created "2018-06-29" @default.
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• W2809565904 date "2018-06-17" @default.
• W2809565904 modified "2023-09-27" @default.
• W2809565904 title "On mod p local-global compatibility for GL3(Qp) in the non-ordinary case" @default.
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• W2809565904 doi "https://doi.org/10.1112/plms.12148" @default.
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