On crystabelline deformation rings of $\mathrm{Gal}({\overline{\mathbb{Q}}}_p/{\mathbb{Q}}_p)$ (with an appendix by Jack Shotton)

Abstract

We prove that certain crystabelline deformation rings of two dimensional residual representations of $\mathrm{Gal}({\overline{\mathbb{Q}}}_p/{\mathbb{Q}}_p)$ are Cohen-Macaulay. As a consequence, this allows to improve Kisin's $R[1/p]=\mathbb{T}[1/p]$ theorem to an $R=\mathbb{T}$ theorem.

57 pages; with an appendix by Jack Shotton; v2 minor revisions after a referee report

References in corpus (1)

• Derived Galois deformation rings