Classicité de formes modulaires surconvergentes

Bijakowski, Stéphane; Pilloni, Vincent; Stroh, Beno ^it

doi:10.4007/annals.2016.183.3.5

Cited by 21 publications

(20 citation statements)

References 23 publications

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“…By Prop.A.3, any element in H 1 (Gal F℘ , σ • χ LT ) is σ-de Rham, which generalizes the well-known fact that any extension of the trivial character by cyclotomic character is de Rham. In fact, suppose F ℘ = Q p , using (7), one can actually calculate: dim E H 1 g,J (Gal F℘ , σ •χ LT ) = d−|J \{σ}|.…”

Section: Appendix a Partially De Rham Trianguline Representationsmentioning

confidence: 99%

“…Since the classical points are Zariski-dense in E and accumulate over the point z h (here one uses the classicality results, e.g. in [7]), the proposition follows from the global triangulation theory [32,Thm.6 We end this section by (conjecturally) constructing some partial de Rham families of Hilbert modular forms as closed subspaces of E ([1, Thm.5.1]). For ℘|p, denote by W ℘ the rigid space over E parameterizing locally Q p -analytic characters of O × ℘ .…”

Section: Appendix a Partially De Rham Trianguline Representationsmentioning

confidence: 99%

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\protect \mathcal{L}-invariants, partially de Rham families, and local-global compatibility

Ding¹

2017

Ann. inst. Fourier

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Let F℘ be a finite extension of Qp. By considering partially de Rham families, we establish a Colmez-Greenberg-Stevens formula (on Fontaine-Mazur L-invariants) for (general) 2-dimensional semi-stable non-crystalline Gal(Qp/F℘)-representations. As an application, we prove local-global compatibility results for completed cohomology of quaternion Shimura curves, and in particular the equality of Fontaine-Mazur L-invariants and Breuil's L-invariants, in critical case. Contents 4. Local-global compatibility 17 4.1. Setup and notations 17 4.2. Completed cohomology and eigenvarieties 18 4.3. Local-global compatibility 25 Appendix A. Partially de Rham trianguline representations 33 References 36

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Section: Appendix a Partially De Rham Trianguline Representationsmentioning

confidence: 99%

Section: Appendix a Partially De Rham Trianguline Representationsmentioning

confidence: 99%

\protect \mathcal{L}-invariants, partially de Rham families, and local-global compatibility

Ding¹

2017

Ann. inst. Fourier

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“…We define in case (C) (these are the normalization factors of [BSP15]). We will use the same symbols to denote the composition with M †χ v,w ֒→ M †χ v ′ ,w .…”

Section: Hecke Operatorsmentioning

confidence: 99%

Eigenvarieties for Cuspforms Over PEL Type Shimura Varieties With Dense Ordinary Locus

Brasca¹

2016

Can. j. math.

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Abstract. Let p > be a prime and let X be a compacti ed PEL Shimura variety of type (A) or (C) such that p is an unrami ed prime for the PEL datum and such that the ordinary locus is dense in the reduction of X. Using the geometric approach of Andreatta, Iovita, Pilloni, and Stevens we de ne the notion of families of overconvergent locally analytic p-adic modular forms of Iwahoric level for X. We show that the system of eigenvalues of any nite slope cuspidal eigenform of Iwahoric level can be deformed to a family of systems of eigenvalues living over an open subset of the weight space. To prove these results, we actually construct eigenvarieties of the expected dimension that parameterize nite slope systems of eigenvalues appearing in the space of families of cuspidal forms.

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“…The method which we use here is by studying the analytic continuation of finite slope overconvergent eigenforms as in [23]. There is a related work [4] of Bijakowski, where classicality results for modular forms over some general PEL type Shimura (with unramified local reductive groups) are proved. Although Bijakowski also used the method of analytic continuation to prove classicality results, there are still many differences between our approach below and that in [4].…”

Section: Analytic Continuation and Classicalitymentioning

confidence: 99%

$p$-adic families of automorphic forms over some unitary Shimura varieties

Shen

2016

Mathematical Research Letters

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Abstract. We construct some n-dimensional eigenvarieties for finite slope overconvergent eigenforms over some unitary Shimura varieties with signature (1, n−1)×(0, n)×· · ·×(0, n) by adapting Andreatta-Iovita-Pilloni's method. We also show that there are some Galois pseudo-characters over our eigenvarieties by studying analytic continuation of finite slope eigenforms over these Shimura varieties.

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Classicité de formes modulaires surconvergentes

Abstract: We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C) associated to an unramified reductive group on $mathbb{Q}_p$. To get this result, we use the analytic continuation method, first used by Buzzard and Kassaei

Cited by 21 publications

References 23 publications

\protect \mathcal{L}-invariants, partially de Rham families, and local-global compatibility

\protect \mathcal{L}-invariants, partially de Rham families, and local-global compatibility

Eigenvarieties for Cuspforms Over PEL Type Shimura Varieties With Dense Ordinary Locus

$p$-adic families of automorphic forms over some unitary Shimura varieties

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