The level 1 weight 2 case of Serre’s conjecture

2 00 7 The level 1 weight 2 case of Serre ’ s conjecture

We prove Serre’s conjecture for the case of Galois representations of Serre’s weight 2 and level 1. We do this by combining the potential modularity results of Taylor and lowering the level for Hilbert modular forms with a Galois descent argument, properties of universal deformation rings, and the non-existence of p-adic Barsotti-Tate conductor 1 Galois representations proved in [Di3].

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The level 1 weight 2 case of Serre ’ s conjecture Luis

We prove Serre’s conjecture for the case of Galois representations of Serre’s weight 2 and level 1. We do this by combining the potential modularity results of Taylor and lowering the level for Hilbert modular forms with a Galois descent argument, properties of universal deformation rings, and the non-existence of p-adic Barsotti-Tate conductor 1 Galois representations proved in [Di3].

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4 The level 1 weight 2 case of Serre ’ s conjecture Luis

We prove Serre’s conjecture for the case of Galois representations with Serre’s weight 2 and level 1. We do this by combining the potential modularity results of Taylor and lowering the level for Hilbert modular forms with a Galois descent argument, properties of universal deformation rings, and the non-existence of p-adic Barsotti-Tate conductor 1 Galois representations proved in [Di3].

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