On level-lowering for mod 2 representations

The theory of “level-lowering” for mod $l$ modular forms is now essentially complete when $l$ is odd, thanks to work of Ribet and others. In the paper [T], Taylor explains how one might be able to attack new cases of Artin’s conjecture if (amongst other things) Wiles' results on lifting of modular mod $l$ Galois representations could be extended to the case $l=2$. One ingredient necessary for such an extension is a level-lowering theorem valid in characteristic 2. In this paper we prove such a theorem, for most mod 2 Galois representations, using, for the most part, Ribet’s ideas. In fact the results here, together with work of Dickinson, Shepherd-Barron and Taylor, enable new cases of Artin’s conjecture to be established (see [BDST]).

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Published 1 January 2000