Let $Z$ be a locally closed subset of a topological space, one denote classically by $\Gamma_{Z}$ the functor of section with support. Let $x$ be a point of the affine space $\mathbb{R}^n$, we denote by $\mathbb{R}_{\mathbb{R}^n}$ the constant sheaf on $\mathbb{R}^n$. Is it true that we can describe $R\Gamma_{\{x\}}\mathbb{R}_{\mathbb{R}^n}$ by $\mathbb{R}_{\{x\}}[-n]$ (obviously this should be valid for a general constant sheaf of $A$-module on $\mathbb{R}^n$ for a ring $A$).
Using the triangle $R\Gamma_{\{x\}}\mathbb{R}_{\mathbb{R}^n}\rightarrow R\Gamma_{\mathbb{R}^n}\mathbb{R}_{\mathbb{R}^n}\rightarrow R\Gamma_{\mathbb{R}^n\setminus\{x\}}\mathbb{R}_{\mathbb{R}^n}\xrightarrow{+1}$, we get immediately that $R\Gamma_{\{x\}}\mathbb{R}_{\mathbb{R}^n}$ is concentrated in degree $n$ and the $H^{n}$ is isomorphic to the $H^{n-1}(R\Gamma_{\mathbb{R}^n\setminus\{x\}})$ which is for me $\mathbb{R}_{\{x\}}$. Are we OK ?