The cohomology of locally analytic representations

Kohlhaase, Jan

doi:10.1515/crelle.2011.013

Cited by 33 publications

(52 citation statements)

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“…Colmez [2010a] and Liu, Xie, and Zhang [Liu et al 2012] determined the spaces of locally analytic vectors of the unitary principal series of GL 2 ‫ޑ(‬ p ) based on this kind of (ϕ, )-module. Our computations of dimensions of Ext 1 an match those of [Kohlhaase 2011] on extensions of locally analytic representations. Nakamura [2009] gave a generalization of Colmez's work in another direction.…”

Section: Introductionsupporting

confidence: 53%

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2013

Algebra Number Theory

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This paper contains a complete proof of Fukaya and Kato's -isomorphism conjecture for invertible -modules (the case of V = V 0 (r ), where V 0 is unramified of dimension 1). Our results rely heavily on Kato's proof, in an unpublished set of lecture notes, of (commutative) -isomorphisms for one-dimensional representations of G ‫ޑ‬ p , but apart from fixing some sign ambiguities in Kato's notes, we use the theory of (φ, )-modules instead of syntomic cohomology. Also, for the convenience of the reader we give a slight modification or rather reformulation of it in the language of Fukuya and Kato and extend it to the (slightly noncommutative) semiglobal setting. Finally we discuss some direct applications concerning the Iwasawa theory of CM elliptic curves, in particular the local Iwasawa Main Conjecture for CM elliptic curves E over the extension of ‫ޑ‬ p which trivialises the p-power division points E( p) of E. In this sense the paper is complimentary to our work with Bouganis (Asian J. Math. 14:3 (2010), 385-416) on noncommutative Main Conjectures for CM elliptic curves.

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Section: Introductionsupporting

confidence: 53%

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2013

Algebra Number Theory

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“…Par dualité, cela prouve que φ → φ , qui est une surjection de LA(O F ), n'admet pas de section continue : on ne peut pas définir de primitive de φ qui dépendent continûment de φ (cf. [22] pour une autre preuve de ce résultat).…”

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Représentations localement analytiques de 𝐺𝐿₂(𝐐_{𝐩}) et (𝜑,Γ)-modules

Colmez

2016

Represent. Theory

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“…However, by construction, E J I (λ, ψ) is just the image of 1 ψ ⊗ E L(λ) J via the above composition. We see that (27) maps ψ to 1 ψ ⊗ E L(λ) J , and the claim follows. We see moreover that…”

Section: Extensions Of Locally Analytic Representations Imentioning

confidence: 65%

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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The cohomology of locally analytic representations

Cited by 33 publications

References 20 publications

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Représentations localement analytiques de 𝐺𝐿₂(𝐐_{𝐩}) et (𝜑,Γ)-modules

Simple ℒ-invariants for GL_{𝓃}

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