The image of the coefficient space in the universal deformation space

TL;DR

This paper investigates the image of the coefficient space within the universal deformation space, which helps understand the structure of finite flat models of Galois representations and their singularities.

Contribution

It explicitly determines the image of the coefficient space in the universal deformation space, providing insight into the resolution of singularities for Galois representations.

Findings

Identified the image of the coefficient space in the universal deformation space.

Clarified the relationship between coefficient space and finite flat models.

Enhanced understanding of the singularity resolution in deformation spaces.

Abstract

The coefficient space is a kind of resolution of singularities of the universal flat deformation space for a given Galois representation of some local field. It parameterizes (in some sense) the finite flat models for the Galois representation. The aim of this note is to determine the image of the coefficient space in the universal deformation space.