Serre weights for quaternion algebras

Toby Gee; David Savitt

doi:10.1112/S0010437X1000518X

Serre weights for quaternion algebras

Toby Gee, David Savitt

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We study the possible weights of an irreducible two-dimensional mod p representation of Gal(F̄/F) which is modular in the sense that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of exceptions.

Original language	English (US)
Pages (from-to)	1059-1086
Number of pages	28
Journal	Compositio Mathematica
Volume	147
Issue number	4
DOIs	https://doi.org/10.1112/S0010437X1000518X
State	Published - Jul 2011

Keywords

Breuil modules
Galois representations
Serre weights
quaternion algebras

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1112/S0010437X1000518X

Cite this

@article{f502051b1dc64c408e374c21be2e0c4d,

title = "Serre weights for quaternion algebras",

abstract = "We study the possible weights of an irreducible two-dimensional mod p representation of Gal({\=F}/F) which is modular in the sense that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of exceptions.",

keywords = "Breuil modules, Galois representations, Serre weights, quaternion algebras",

author = "Toby Gee and David Savitt",

year = "2011",

month = jul,

doi = "10.1112/S0010437X1000518X",

language = "English (US)",

volume = "147",

pages = "1059--1086",

journal = "Compositio Mathematica",

issn = "0010-437X",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - Serre weights for quaternion algebras

AU - Gee, Toby

AU - Savitt, David

PY - 2011/7

Y1 - 2011/7

N2 - We study the possible weights of an irreducible two-dimensional mod p representation of Gal(F̄/F) which is modular in the sense that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of exceptions.

AB - We study the possible weights of an irreducible two-dimensional mod p representation of Gal(F̄/F) which is modular in the sense that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of exceptions.

KW - Breuil modules

KW - Galois representations

KW - Serre weights

KW - quaternion algebras

UR - http://www.scopus.com/inward/record.url?scp=80053129597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053129597&partnerID=8YFLogxK

U2 - 10.1112/S0010437X1000518X

DO - 10.1112/S0010437X1000518X

M3 - Article

AN - SCOPUS:80053129597

SN - 0010-437X

VL - 147

SP - 1059

EP - 1086

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 4

ER -

Serre weights for quaternion algebras

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this