A note on reductions of 2-dimensional crystalline Galois representations

Details A note on reductions of 2-dimensional crystalline Galois representations A note on reductions of 2-dimensional crystalline Galois representations

2012-02-26

arxiv.org/abs/1202.5711v1

Mathematics

Number Theory

Scientific paper

Let p be an odd prime number, K_{f} the finite unramified extension of \mathbb{Q}_{p} of degree f, and G_{K_{f}} its absolute Galois group. We construct analytic families of \'etale (\phi,{\Gamma})-modules which give rise to some families of 2-dimensional crystalline representations of G_{K_{f}} with largest Hodge-Tate weight at least p. As an application, we prove that the modulo p reductions of the members of each such family (with respect to appropriately chosen Galois-stable lattices) are constant.

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