Why are formal schemes assumed to be (locally) noetherian?

All sources that I know that study formal schemes seem to assume that they are locally noetherian. For instance, in Hartshorne “Algebraic Geometry”, the author states: “For technical reasons we will limit our discussion to noetherian schemes”.

What are these technical reasons? what basic facts about formal schemes fail if they are not noetherian (or not locally noetherian)?


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