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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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