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Let $R$ be a deformation ring and $M$ be a finitely generated $R$-module. A strategy for proving the theorems $R=T$ is to associate with $(R,M)$ a Taylor-Wiles system denoted $(R_{Q},M_{Q})$. Here I'm ...

My question is maybe going to be a bit vague. My apologies if so. The setting: Let $\overline{\rho}$ be a residual representation and $R$ be a deformation ring of $\overline{\rho}$. Let $\mathbb{T}$ ...

Let $\bar{\rho}_p$ be a two-dimensional irreducible local Galois representation of $Gal(\bar{\mathbb{Q}}_p / \mathbb{Q}_p)$ on a $k$-vector space, where $k$ is a finite extension of $\mathbb{F}_p$. ...