Formal spectrum ($\mathrm{Spf}A$)

For a complete ring with an adic topology defined by $I$, the formal spectrum has the prime ideals containing $I$ as its points and structure sheaf ${\underleftarrow{\lim }}_n{\mathcal{O}}_{\mathrm{Spec}(A/I^{n+1})}$. On a principal open subset $D(f)$ its sections form the completed localization of an adic ring, not generally the ordinary localization $A_f$.

// Target: ringed-space.bigb