For general affinoid domain $\mathfrak{M}(\mathcal{A})$ with general affinoid domains covering $\mathfrak{V}$, the complex $C^{\centerdot}(\mathcal{A},\mathfrak{V})$ is acyclic. So is $C^{\centerdot}(M,\mathfrak{V})$ for finite Banach $\mathcal{A}$-module $M$. ([Ber, Proposition 2.2.5])