Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes

C. Breuil; Fred Diamond

doi:10.24033/asens.2230

Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes

Translated title of the contribution: Hilbert modular forms modulo p and values of Galois extensions

C. Breuil, Fred Diamond

Univ Paris 11, Lab Math Orsay

Research output: Working paper/Preprint › Preprint

35 Citations (Scopus)

208 Downloads (Pure)

Abstract

Let F be a totally real field, v an unramified place of F dividing p and ρ an irreducible two-dimensional mod p Galois representation of the absolute Galois group of F. Suppose that ρ restricted to a decomposition group at v is reducible and sufficiently generic. If ρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of the decomposition group in terms of the action of GL₂(F_v) on the cohomology mod p.

Translated title of the contribution	Hilbert modular forms modulo p and values of Galois extensions
Original language	French
Publisher	Societe Mathematique de France
Number of pages	74
DOIs	https://doi.org/10.24033/asens.2230
Publication status	Published - 27 Aug 2012

Publication series

Name	Annales Scientifiques de l'Ecole Normale Superieure
Volume	47

Access to Document

10.24033/asens.2230

Formes modulaires de Hilbert_BREUIL_PUblished27August2012_GREEN AAMAccepted author manuscript, 800 KB

http://arxiv.org/abs/1208.5367

Cite this

@techreport{44253982a66b48a283bc6e97669988c7,

title = "Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes",

abstract = "Let F be a totally real field, v an unramified place of F dividing p and ρ an irreducible two-dimensional mod p Galois representation of the absolute Galois group of F. Suppose that ρ restricted to a decomposition group at v is reducible and sufficiently generic. If ρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of the decomposition group in terms of the action of GL2(Fv) on the cohomology mod p.",

author = "C. Breuil and Fred Diamond",

year = "2012",

month = aug,

day = "27",

doi = "10.24033/asens.2230",

language = "French",

series = "Annales Scientifiques de l'Ecole Normale Superieure",

publisher = "Societe Mathematique de France",

address = "France",

type = "WorkingPaper",

institution = "Societe Mathematique de France",

}

TY - UNPB

T1 - Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes

AU - Breuil, C.

AU - Diamond, Fred

PY - 2012/8/27

Y1 - 2012/8/27

N2 - Let F be a totally real field, v an unramified place of F dividing p and ρ an irreducible two-dimensional mod p Galois representation of the absolute Galois group of F. Suppose that ρ restricted to a decomposition group at v is reducible and sufficiently generic. If ρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of the decomposition group in terms of the action of GL2(Fv) on the cohomology mod p.

AB - Let F be a totally real field, v an unramified place of F dividing p and ρ an irreducible two-dimensional mod p Galois representation of the absolute Galois group of F. Suppose that ρ restricted to a decomposition group at v is reducible and sufficiently generic. If ρ is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of the decomposition group in terms of the action of GL2(Fv) on the cohomology mod p.

U2 - 10.24033/asens.2230

DO - 10.24033/asens.2230

M3 - Preprint

T3 - Annales Scientifiques de l'Ecole Normale Superieure

BT - Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes

PB - Societe Mathematique de France

ER -

Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes

Abstract

Publication series

Access to Document

Fingerprint

Cite this