On reductions of families of crystalline Galois representations

  • Gerasimos Dousmanis

On reductions of families of crystalline Galois representations cover
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Abstract

Let KfK_f be the finite unramified extension of Qp{Q}_p of degree ff and EE any finite large enough coefficient field containing Kf.K_f. We construct analytic families of étale (φ,Γ)(\varphi ,\Gamma )-modules which give rise to families of crystalline EE-representations of the absolute Galois group GKfG_{K_f} of Kf.K_f. For any irreducible effective two-dimensional crystalline EE-representation of GKfG_{K_f} with labeled Hodge-Tate weights 0,kiτi{0,-k_i}_{\tau _i} induced from a crystalline character of GK2f,G_{K_{2f}}, we construct an infinite family of crystalline EE -representations of GKfG_{K_f} of the same Hodge-Tate type which contains it. As an application, we compute the semisimplified mod pp reductions of the members of each such family.

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Gerasimos Dousmanis, On reductions of families of crystalline Galois representations. Doc. Math. 15 (2010), pp. 873–938

DOI 10.4171/DM/317