ScalingStacks

Lemma 2.61. Let $V$ be an affinoid domain in $\mathfrak{M}(\mathcal{A})$. Then $V$ is homeomorphic to $\mathfrak{M}(\mathcal{A}_{V})$. Moreover $\mathcal{A}_{V}$ is a flat $\mathcal{A}$-algebra. ([Ber, Proposition 2.2.4])