On the Modularity of Wildly Ramified Galois Representations

Details On the Modularity of Wildly Ramified Galois Representations On the Modularity of Wildly Ramified Galois Representations

2004-11-09

arxiv.org/abs/math/0411214v1

Mathematics

Number Theory

31 pages

Scientific paper

We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. Such a family contains the original example studied by Buhler. In the process, we prove that an infinite family of residually modular Galois representations are modular by studying $\Lambda$-adic Hecke algebras.

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