Types of Schemes
There are many ways one can qualify a scheme. According to a basic idea of Grothendieck, conditions should be applied to a morphism of schemes. Any scheme S has a unique morphism to Spec(Z), so this attitude, part of the relative point of view, doesn't lose anything.
For detail on the development of scheme theory, which quickly becomes technically demanding, see first glossary of scheme theory.
Read more about this topic: Scheme (mathematics)
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