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Lifting modular mod \(l\) representations. (English) Zbl 0809.11025
The article extends previous work of the authors and others. The main result is that once a modulo \(l\) (odd prime) Galois representation has a modular lift to characteristic zero, then one can find another such lift with prescribed restriction to the decomposition groups at primes \(p\neq l\). The proof uses a careful analysis of the possible local representations and the Jacquet-Langlands correspondence.
Reviewer: G.Faltings (Bonn)

MSC:
11F11 Holomorphic modular forms of integral weight
11F80 Galois representations
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