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

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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.",

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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

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M3 - Article

AN - SCOPUS:80053129597

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JF - Compositio Mathematica

IS - 4

ER -

Serre weights for quaternion algebras

Abstract

Keywords

ASJC Scopus subject areas

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