nLab Demazure, lectures on p-divisible groups, I.7. operations on formal schemes

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A finite limit of kk-formal schemes is kk-formal. The category of kk-formal schemes has arbitrary products.

A formal kk-scheme is called local kk-scheme if it is the formal spectrum of a local ring (=has a unique maximal ideal).

Any formal kk-scheme is a coproduct of local kk-schemes (Demazure, p.15).

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