Duke Mathematical Journal

Serre's modularity conjecture: The level one case

Chandrashekhar Khare

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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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Duke Math. J., Volume 134, Number 3 (2006), 557-589.

First available in Project Euclid: 28 August 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F80: Galois representations 11F11: Holomorphic modular forms of integral weight
Secondary: 11R39: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]


Khare, Chandrashekhar. Serre's modularity conjecture: The level one case. Duke Math. J. 134 (2006), no. 3, 557--589. doi:10.1215/S0012-7094-06-13434-8. https://projecteuclid.org/euclid.dmj/1156771903

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