Lifting modular mod \(l\) representations. (English) Zbl 0809.11025

Diamond, Fred; Taylor, Richard

Duke Math. J. 74, No. 2, 253-269 (1994).

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

Keywords:

modular forms; Galois representation; modular lift; Jacquet-Langlands correspondence

References:

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