Ordinary local representations and $\text{Ext}$ groups

We can associate an admissible unitary representation $\mathrm{\Pi }({\rho }_p)$ of ${\text{GL}}_2({\text{Q}}_p)$ with every local Galois representation ${\rho }_p$ by the $p$-adic local Langlands correspondence. If ${\rho }_p$ is ordinary, we prove local and global vanishing results for $\text{Ext}$ functors with respect to these representations.