Classicité de formes modulaires surconvergentes

Bijakowski, Stéphane

doi:10.48550/arxiv.1212.2035

Cited by 2 publications

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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%

“…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]. Namely, Bijakowski studied intensively the geometry near the region with integer degrees in the rigid analytic Shimura varieties, while we are mainly based on the geometry of the special fiber, which is simpler in our special case.…”

Section: Analytic Continuation and Classicalitymentioning

confidence: 99%

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$p$-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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Section: Analytic Continuation and Classicalitymentioning

confidence: 99%

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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“…Si u : G ÝÑ G 1 est un morphisme qui devient un isomorphisme en fibre générique, alors Deg τ pG 1 q ě Deg τ pGq, avec égalité si et seulement si u est un isomorphisme.Démonstration. -Voir[Bij12] Proposition 1.19.…”

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La filtration canonique des $${{\mathcal {O}}}$$ O -modules p-divisibles

Hernandez

2019

Math. Ann.

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In this article we associate to G, a truncated p-divisible O-module of given signature, where O is a finite unramified extension of Zp, a filtration of G by sub-O-modules under the conditions that his Hasse µ-invariant is smaller than an explicite bound. This filtration generalise the one given when G is µ-ordinary. The construction of the filtration relies on a precise study of the cristalline periods of a p-divisible O-module. We then apply this result to families of such groups, in particular to stricts neighbourhoods of the µ-ordinary locus inside some PEL Shimura varieties.Résumé. -Dans cet article, à G un groupe p-divisible tronqué muni d'une action d'une extension finie non ramifiée O de Zp, et de signature donnée, on associe sous une condition explicite sur son µ-invariant de Hasse, une filtration de G par des sous-O-modules qui étend la filtration canonique lorsque G est µ-ordinaire. La construction se fait en étudiant les périodes cristallines des groupes p-divisibles avec action de O. On applique ensuite cela aux familles de tels groupes, en particulier des voisinages stricts du lieu µ-ordinaire dans des variétés de Shimura PEL.

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Classicité de formes modulaires surconvergentes

Cited by 2 publications

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

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

La filtration canonique des $${{\mathcal {O}}}$$ O -modules p-divisibles

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