On reductions of families of crystalline Galois representations

Details On reductions of families of crystalline Galois representations On reductions of families of crystalline Galois representations

2008-05-12

arxiv.org/abs/0805.1634v4

Mathematics

Number Theory

Final version. To appear in Documenta Math

Scientific paper

Let K_{f} be the finite unramified extension of Q_{p} of degree f and E any finite large enough coefficient field containing K_{f}. We construct analytic families of \'etale (Phi,Gamma)-modules which give rise to families of crystalline E-representations of the absolute Galois group G_{K_{f}} of K_{f}. For any irreducible effective two-dimensional crystalline E-representation of G_{K_{f}} with labeled Hodge-Tate weights {0,-k_{i}}_{{\tau}_{i}} induced from a crystalline character of G_{K_{2f}}, we construct an infinite family of crystalline E-representations of G_{K_{f}} of the same Hodge-Tate type which contains it. As an application, we compute the semisimplified mod p reductions of the members of each such family.

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