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15 September 2006 Serre's modularity conjecture: The level one case
Chandrashekhar Khare
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Duke Math. J. 134(3): 557-589 (15 September 2006). DOI: 10.1215/S0012-7094-06-13434-8

Abstract

We prove the level one case of Serre's conjecture. Namely, we prove that any continuous, odd, irreducible representation ρ̲:GQGL2(Fp̲) which is unramified outside p arises from a cuspidal eigenform in Sk(SL2(Z)) for some integer k2. The proof relies on the methods introduced in an earlier joint work with J.-P. Wintenberger [31] together with a new method of weight reduction

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Chandrashekhar Khare. "Serre's modularity conjecture: The level one case." Duke Math. J. 134 (3) 557 - 589, 15 September 2006. https://doi.org/10.1215/S0012-7094-06-13434-8

Information

Published: 15 September 2006
First available in Project Euclid: 28 August 2006

zbMATH: 1105.11013
MathSciNet: MR2254626
Digital Object Identifier: 10.1215/S0012-7094-06-13434-8

Subjects:
Primary: 11F11 , 11F80
Secondary: 11R39

Rights: Copyright © 2006 Duke University Press

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Vol.134 • No. 3 • 15 September 2006
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