Density of potentially crystalline representations of fixed weight

Abstract

Let K be a finite extension of Qp. We fix a continuous absolutely irreducible representation of the absolute Galois group of K over a finite dimensional vector space with coefficient in a finite field of characteristic p and consider its universal deformation ring R. If we fix a regular set of Hodge-Tate weights k, we prove, under some hypothesis, that the closed points of Spec(R[1/p]) corresponding to potentially crystalline representations of fixed Hodge-Tate weights k are dense in Spec(R[1/p]) for the Zariski topology.

We fixed a gap in the proof of previous Cor 3.7, now Theorem 4.11, and fixed some sign errors

References in corpus (2)

• Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p
• Families of trianguline representations and finite slope spaces

Cited by in corpus (6)

• On local Galois deformation rings
• Frobenius modules over multivariate Robba rings
• Density of automorphic points in deformation rings of polarized global Galois representations
• On the automorphy of 2-dimensional potentially semi-stable deformation rings of $G_{{\mathbb{Q}}_p}$
• Smoothness and Classicality on eigenvarieties
• Companion points on the eigenvariety with non-regular weights