Inventiones mathematicae

, 178:485

Serre’s modularity conjecture (I)


DOI: 10.1007/s00222-009-0205-7

Cite this article as:
Khare, C. & Wintenberger, JP. Invent. math. (2009) 178: 485. doi:10.1007/s00222-009-0205-7


This paper is the first part of a work which proves Serre’s modularity conjecture. We first prove the cases \(p\not=2\) and odd conductor, and p=2 and weight 2, see Theorem 1.2, modulo Theorems 4.1 and 5.1. Theorems 4.1 and 5.1 are proven in the second part, see Khare and Wintenberger (Invent. Math., doi:10.1007/s00222-009-0206-6, 2009). We then reduce the general case to a modularity statement for 2-adic lifts of modular mod 2 representations. This statement is now a theorem of Kisin (Invent. Math., doi:10.1007/s00222-009-0207-5, 2009).

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Chandrashekhar Khare
    • 1
  • Jean-Pierre Wintenberger
    • 2
  1. 1.Department of Mathematics University of UtahSalt Lake CityUSA
  2. 2.Département de MathématiqueUniversité de StrasbourgStrasbourg CedexFrance
  3. 3.Department of MathematicsUCLALos AngelesUSA