Reduction modulo p of cuspidal representations and weights in Serre's conjecture

Michael M. Schein

doi:10.1112/blms/bdn117

Reduction modulo p of cuspidal representations and weights in Serre's conjecture

Michael M. Schein

Department of Mathematics

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

6 Scopus citations

Abstract

Let script O sign be the ring of integers of a p-adic field and its maximal ideal. This paper computes the Jordan-Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(script O sign/ ^e) for e ≥ 1. An alternative formulation of Serre's conjecture for Hilbert modular forms is then provided.

Original language	English
Pages (from-to)	147-154
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	41
Issue number	1
DOIs	https://doi.org/10.1112/blms/bdn117
State	Published - Feb 2009

Bibliographical note

Funding Information:
Acknowledgements. The author is very grateful to the referee for comments that improved the exposition, and particularly for an observation that considerably simplified the computations in Section 2. He is grateful to Ron Livné and the Golda Meir Fellowship Trust for supporting this research.

Access to Document

10.1112/blms/bdn117

Cite this

@article{9c4f4462e5bd467f9a5b05f56bc95d97,

title = "Reduction modulo p of cuspidal representations and weights in Serre's conjecture",

abstract = "Let script O sign be the ring of integers of a p-adic field and its maximal ideal. This paper computes the Jordan-H{\"o}lder decomposition of the reduction modulo p of the cuspidal representations of GL2(script O sign/ e) for e ≥ 1. An alternative formulation of Serre's conjecture for Hilbert modular forms is then provided.",

author = "Schein, {Michael M.}",

note = "Funding Information: Acknowledgements. The author is very grateful to the referee for comments that improved the exposition, and particularly for an observation that considerably simplified the computations in Section 2. He is grateful to Ron Livn{\'e} and the Golda Meir Fellowship Trust for supporting this research.",

year = "2009",

month = feb,

doi = "10.1112/blms/bdn117",

language = "אנגלית",

volume = "41",

pages = "147--154",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - Reduction modulo p of cuspidal representations and weights in Serre's conjecture

AU - Schein, Michael M.

N1 - Funding Information: Acknowledgements. The author is very grateful to the referee for comments that improved the exposition, and particularly for an observation that considerably simplified the computations in Section 2. He is grateful to Ron Livné and the Golda Meir Fellowship Trust for supporting this research.

PY - 2009/2

Y1 - 2009/2

N2 - Let script O sign be the ring of integers of a p-adic field and its maximal ideal. This paper computes the Jordan-Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(script O sign/ e) for e ≥ 1. An alternative formulation of Serre's conjecture for Hilbert modular forms is then provided.

AB - Let script O sign be the ring of integers of a p-adic field and its maximal ideal. This paper computes the Jordan-Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(script O sign/ e) for e ≥ 1. An alternative formulation of Serre's conjecture for Hilbert modular forms is then provided.

UR - http://www.scopus.com/inward/record.url?scp=60749085405&partnerID=8YFLogxK

U2 - 10.1112/blms/bdn117

DO - 10.1112/blms/bdn117

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:60749085405

SN - 0024-6093

VL - 41

SP - 147

EP - 154

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -

Reduction modulo p of cuspidal representations and weights in Serre's conjecture

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this