On level-lowering for mod 2 representations
Kevin Buzzard · Mathematical Research Letters · 2000
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]).