3 problems

Let $R_\rho^{\mathrm{ord}}$ be the ordinary deformation ring and let $H^2_{\mathcal P_{\mathrm{ord}}}(\operatorname{Gal}_{\mathbb Q,\Sigma},\operatorname{Lie}\check{\mathrm G})$ de…

Let $R_\rho^{\mathrm{ord}}$ be the ordinary deformation ring attached to the Galois representation $\rho$ and let $\Lambda_E$ be the ordinary weight algebra, with…

Let $\pi$ be the ordinary cuspidal automorphic representation and let $\check{\mathrm G}$ be a smooth $\mathbb Z_p$-model of the dual group. Let $E$ be the coefficient field,…