English

Density of potentially crystalline representations of fixed weight

Number Theory 2019-02-20 v2 Representation Theory

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.

Keywords

Cite

@article{arxiv.1311.3249,
  title  = {Density of potentially crystalline representations of fixed weight},
  author = {Eugen Hellmann and Benjamin Schraen},
  journal= {arXiv preprint arXiv:1311.3249},
  year   = {2019}
}

Comments

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