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Title of Journal: Invent math

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Abbravation: Inventiones mathematicae

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Springer-Verlag

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10.1007/bf00530786

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1432-1297

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Serre’s modularity conjecture I

Authors: Chandrashekhar Khare JeanPierre Wintenberger
Publish Date: 2009/07/04
Volume: 178, Issue: 3, Pages: 485-
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Abstract

This paper is the first part of a work which proves Serre’s modularity conjecture We first prove the cases pnot=2 and odd conductor and p=2 and weight 2 see Theorem 12 modulo Theorems 41 and 51 Theorems 41 and 51 are proven in the second part see Khare and Wintenberger Invent Math doi 101007/s0022200902066 2009 We then reduce the general case to a modularity statement for 2adic lifts of modular mod 2 representations This statement is now a theorem of Kisin Invent Math doi 101007/s0022200902075 2009

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Other Papers In This Journal:
  1. Serre’s modularity conjecture (I)
  2. Erratum to: Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space
  3. Image of Λ -adic Galois representations modulo p
  4. Representation theory of $\mathcal{W}$-algebras
  5. The Kodaira dimension of the moduli of K3 surfaces
  6. Brownian Gibbs property for Airy line ensembles
  7. Degree formula for connective K -theory
  8. Some quantitative results in $${\mathcal {C}}^0$$ symplectic geometry
  9. Convexes divisibles IV : Structure du bord en dimension 3
  10. The classification of irreducible admissible mod p representations of a p -adic GL n
  11. Some prime factorization results for type II 1 factors
  12. $\mathcal{C}^{2}$ surface diffeomorphisms have symbolic extensions
  13. On the weights of mod p Hilbert modular forms
  14. Operator-algebraic superridigity for SL n (ℤ), n ≥3
  15. Exceptional zero formulae and a conjecture of Perrin-Riou
  16. F-singularities of pairs and Inversion of Adjunction of arbitrary codimension
  17. Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case
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