2018
DOI: 10.1093/imrn/rnx287
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Some Results on the Locally Analytic Socle for $\textrm{GL}_{n}(\mathbb {Q}_{p})$

Abstract: We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuil's locally analytic socle conjecture for GLn(Qp).which is a Banach space over E equipped with a continuous action of G(Q p ) ∼ = GL 3 (Q p ) (this isomorphism depends on the choice of u), and a continuous action of (commutative) Hecke algebra H p outside p. The action of H p commutes with that of GL… Show more

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Cited by 3 publications
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“…be the parabolic with component labelled by our fixed place v equal to the upper triangular Borel and other components equal to the whole group GL 2 . See, for example, [Din18] for another application of eigenvarieties defined with respect to a nonminimal parabolic. We also note that partial Hilbert modular eigenvarieties have been used recently by Barrera, Dimitrov and Jorza to study the exceptional zero conjecture for Hilbert modular forms [BDJ17].…”
Section: A Halo For the Partial Eigenvarietymentioning
confidence: 99%
“…be the parabolic with component labelled by our fixed place v equal to the upper triangular Borel and other components equal to the whole group GL 2 . See, for example, [Din18] for another application of eigenvarieties defined with respect to a nonminimal parabolic. We also note that partial Hilbert modular eigenvarieties have been used recently by Barrera, Dimitrov and Jorza to study the exceptional zero conjecture for Hilbert modular forms [BDJ17].…”
Section: A Halo For the Partial Eigenvarietymentioning
confidence: 99%