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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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##### References:
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