, Volume 178, Issue 3, pp 505-586
Date: 04 Jul 2009

Serre’s modularity conjecture (II)

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We provide proofs of Theorems 4.1 and 5.1 of Khare and Wintenberger (Invent. Math., doi:10.1007/s00222-009-0205-7, 2009).

Dedicated to Jean-Pierre Serre
CK was partially supported by NSF grants DMS 0355528 and DMS 0653821, the Miller Institute for Basic Research in Science, University of California Berkeley, and a Guggenheim fellowship.
JPW is member of the Institut Universitaire de France.