# On the Modularity of Wildly Ramified Galois Representations

Research paper by Edray Herber Goins

Indexed on: 09 Nov '04Published on: 09 Nov '04Published in: Mathematics - Number Theory

#### Abstract

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.