ScalingStacks

Definition 2.72. For any open subset $U$ of $\mathfrak{M}(\mathcal{A})$, let $\mathscr{O}_{\mathfrak{M}(\mathcal{A})}$ be the pre-sheaf of $k$-algebras (with respect to the canonical topology) which assigns $U$ the limit

$$\mathscr{O}_{\mathfrak{M}(\mathcal{A})}(U):=\varprojlim_{V\subset U,\text{V special domain}}\mathcal{A}_{V}$$

It is also a sheaf thanks to the compactness of special domains under canonical topology. This is called the structural sheaf of $\mathfrak{M}(\mathcal{A})$.