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Absolute irreducibility implies free action on framed universal deformation ring

Let $\overline{\rho}: G\longrightarrow \text{GL}_n(\mathbb{F}_p)$ be a residual representation of the Galois group of a number field. Let $R_{\overline{\rho}}^{\square,\text{univ}}$ be the universal ...
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galois deformation ring with type is union of irreducible components

Notation: $K$ finite extension of $\mathbb{Q}_p$, $G_K$ absolute Galois group of $K$, $E$ is finite extension of $\mathbb{Q}_p$ (coefficient field), $O_E$ is ring of integer in $E$. In this paper of ...
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