Serre’s modularity conjecture (I)

This paper is the first part of a work which proves Serre’s modularity conjecture. We first prove the cases 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: 10.1...

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Bibliographic Details
Published in:Inventiones mathematicae 2009-12, Vol.178 (3), p.485-504
Main Authors: Khare, Chandrashekhar, Wintenberger, Jean-Pierre
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Modularity
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Summary:This paper is the first part of a work which proves Serre’s modularity conjecture. We first prove the cases 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 ).
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-009-0205-7