Vers le socle localement analytique pour $${\mathrm {GL}}_n$$ GL n II

Breuil, Christophe

doi:10.1007/s00208-014-1086-7

Cited by 33 publications

(82 citation statements)

References 14 publications

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“…. By Lemma 4.6 (which also holds if the m y -eigenspace is replaced by the m y -generalized eigenspace) and [8,Cor. 3.4], we deduce f ′ −f = 0.…”

Section: Local-global Compatibilitymentioning

confidence: 85%

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Simple ℒ-invariants for GL_{𝓃}

Ding

2019

Trans. Amer. Math. Soc.

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Let L be a finite extension of Q p , and ρ L be an n-dimensional semi-stable non crystalline p-adic representation of Gal L with full monodromy rank. Via a study of Breuil's (simple) L-invariants, we attach to ρ L a locally Q p -analytic representation Π(ρ L ) of GL n (L), which carries the exact information of the Fontaine-Mazur simple L-invariants of ρ L . When ρ L comes from an automorphic representation of G(A F + ) (for a unitary group G over a totally real filed F + which is compact at infinite places and GL n at p-adic places), we prove under mild hypothesis that Π(ρ L ) is a subrerpresentation of the associated Hecke-isotypic subspaces of the Banach spaces of p-adic automorphic forms on G(A F + ). In other words, we prove the equality of Breuil's simple L-invariants and Fontaine-Mazur simple L-invariants.

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“…. By Lemma 4.6 (which also holds if the m y -eigenspace is replaced by the m y -generalized eigenspace) and [8,Cor. 3.4], we deduce f ′ −f = 0.…”

Section: Local-global Compatibilitymentioning

confidence: 85%

“…(a) By Lemma 4.6,[6, Thm. 4.3] and[8, Cor. 3.4], one can deduce any non-zero map f in the left hand side set factors through St an n (α, λ), and induces a non-zero map St ∞ n (α, λ) ֒→ Π R∞−an Cor.…”

mentioning

confidence: 99%

Simple ℒ-invariants for GL_{𝓃}

Ding

2019

Trans. Amer. Math. Soc.

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“…(We note that [Bre15] works with the group of L-points of a split reductive group over L. However, the proofs work unchanged for our group G. See also [BHS17a, Rk. 5.1.2].)…”

Section: A Partial Adjunctionmentioning

confidence: 99%

“…2.5] we have that C(w alg , w) = F G B (L(w alg ·(−λ)), π B,F ) is the (irreducible) socle of PS(w alg , F). (We remark that for us, the construction of Orlik-Strauch, as well as the dot action of W on X(T ), are defined relative to our choice of lower-triangular Borel subgroup B, just as in [Bre15]. In [Bre16] the dot action was defined relative to B.)…”

Section: 1mentioning

confidence: 99%

Towards the Finite Slope Part for GLn

Breuil

Herzig

2019

International Mathematics Research Notices

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Let L be a finite extension of Qp and n ≥ 2. We associate to a crystabelline n-dimensional representation of Gal(L/L) satisfying mild genericity assumptions a finite length locally Qp-analytic representation of GLn(L). In the crystalline case and in a global context, using the recent results on the locally analytic socle from [BHS17a] we prove that this representation indeed occurs in spaces of p-adic automorphic forms. We then use this latter result in the ordinary case to show that certain "ordinary" p-adic Banach space representations constructed in our previous work appear in spaces of p-adic automorphic forms. This gives strong new evidence to our previous conjecture in the p-adic case.

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“…Remark 2.3. It may be advantageous to see the critical type of a triangulation as lying in the Weyl group of Res K/Qp GL n (see [14,16]).…”

mentioning

confidence: 99%

Smoothness of definite unitary eigenvarieties at critical points

Bergdall

2018

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in terms of "critical types" and when our bound is minimized it matches the dimension of the eigenvariety. In those cases, which we explicitly determine, the eigenvariety is necessarily smooth and our proof also shows that the completed local ring on the eigenvariety is naturally a certain universal Galois deformation ring.

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Vers le socle localement analytique pour $${\mathrm {GL}}_n$$ GL n II

Cited by 33 publications

References 14 publications

Simple ℒ-invariants for GL_{𝓃}

Simple ℒ-invariants for GL_{𝓃}

Towards the Finite Slope Part for GLn

Smoothness of definite unitary eigenvarieties at critical points

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