THE WEIGHT PART of SERRE'S CONJECTURE for GL(2)

Toby Gee; Tong Liu; David Savitt

doi:10.1017/fmp.2015.1

THE WEIGHT PART of SERRE'S CONJECTURE for GL(2)

Toby Gee
, Tong Liu
, David Savitt

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

36 Scopus citations

Abstract

Let p>2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti-Tate representations, over arbitrary finite extensions of Q_p. As a consequence, we establish (under the usual Taylor-Wiles hypothesis) the weight part of Serre's conjecture for GL(2) over arbitrary totally real fields.

Original language	English (US)
Article number	e2
Journal	Forum of Mathematics, Pi
Volume	3
DOIs	https://doi.org/10.1017/fmp.2015.1
State	Published - Jan 1 2015
Externally published	Yes

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1017/fmp.2015.1

Cite this

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title = "THE WEIGHT PART of SERRE'S CONJECTURE for GL(2)",

abstract = "Let p>2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti-Tate representations, over arbitrary finite extensions of Qp. As a consequence, we establish (under the usual Taylor-Wiles hypothesis) the weight part of Serre's conjecture for GL(2) over arbitrary totally real fields.",

author = "Toby Gee and Tong Liu and David Savitt",

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AU - Savitt, David

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N2 - Let p>2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti-Tate representations, over arbitrary finite extensions of Qp. As a consequence, we establish (under the usual Taylor-Wiles hypothesis) the weight part of Serre's conjecture for GL(2) over arbitrary totally real fields.

AB - Let p>2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti-Tate representations, over arbitrary finite extensions of Qp. As a consequence, we establish (under the usual Taylor-Wiles hypothesis) the weight part of Serre's conjecture for GL(2) over arbitrary totally real fields.

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UR - https://www.scopus.com/pages/publications/84998895375#tab=citedBy

U2 - 10.1017/fmp.2015.1

DO - 10.1017/fmp.2015.1

M3 - Article

AN - SCOPUS:84998895375

SN - 2050-5086

VL - 3

JO - Forum of Mathematics, Pi

JF - Forum of Mathematics, Pi

M1 - e2

ER -

THE WEIGHT PART of SERRE'S CONJECTURE for GL(2)

Abstract

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