We give a criterion for two -adic Galois representations of an algebraic number field to be isomorphic when restricted to a decomposition group, in terms of the global representations mod . This is applied to prove a generalization of a conjecture of Rasmussen-Tamagawa under a semistablity condition, extending some results of one of the authors. It is also applied to prove a congruence result on the Fourier coefficients of modular forms.
Cite this article
Yoshiyasu Ozeki, Yuichiro Taguchi, On Congruences of Galois Representations of Number Fields. Publ. Res. Inst. Math. Sci. 50 (2014), no. 2, pp. 287–306DOI 10.4171/PRIMS/134