Local Compatibility for Trianguline Representations

Abstract: Trianguline representations are a big class of $p$-adic representations that contain all nice enough (cristalline) ones but allow a continuous variation of weights. Global consideration suggests that the $GL_2(\mathbb{Q}_p)$ representation arising from a trianguline representation should have nonzero eigenspace under Emerton's Jacquet functor. We prove this result using purely local method as well as a generalization to $p$-adic representation of $G_F$ for $F$ unramified over $\mathbb{Q}_p$.

Mathematics

Audience: researchers in the topic

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PKU/BICMR Number Theory Seminar