Formal spectrum
= Formal spectrum
{title2=$\operatorname{Spf}A$}
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 $\varprojlim_n\mathcal O_{\operatorname{Spec}(A/I^{n+1})}$. 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