On reductions of families of crystalline Galois representations

2008/05/12 by Dousmanis, Gerasimos
#11F80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0805.1634

Abstract

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 (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_τ_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.

Related

• A note on reductions of 2-dimensional crystalline Galois representations
• Reductions of Some Crystalline Representations in the Unramified Setting
• Reductions of Crystalline Representations for Small Weights
• Crystalline representations of G_Qp^a with coefficients
• Construction of some families of 2-dimensional crystalline representations