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On reductions of families of crystalline Galois representations

On reductions of families of crystalline Galois representations

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 étale (\varphi ,\Gamma ) -modules which give rise to families of crystalline E -representations of the absolute Galois group G_{K_f} of K_f. For …