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

Mathematics

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

31 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

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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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.",

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

Abstract

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