$\mathscr{O}_{\mathfrak{M}(\mathcal{A})}$ is a sheaf of local rings. The topological space $\mathfrak{M}(\mathcal{A})$ has a structure of locally ringed space given by the sheaf $\mathscr{O}_{\mathfrak{M}(\mathcal{A})}$. ([Ber, Section 2.3])