Journal
MATHEMATISCHE ANNALEN
Volume 373, Issue 3-4, Pages 1341-1427Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00208-018-1742-4
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We generalize results of Clozel, Harris and Taylor by proving modularity lifting theorems for ordinary l-adic Galois representations of any dimension of an imaginary CM or totally real number field. The main theorems are obtained by establishing an Rred=T theorem over a Hida family. A key part of the proof is to construct appropriate ordinary lifting rings at the primes dividing l and to determine their irreducible components.
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