Properties of Scheme Morphisms
One of Grothendieck's fundamental ideas is to emphasize relative notions, i.e. conditions on morphisms rather than conditions on schemes themselves. The category of schemes has a final object, the spectrum of the ring of integers; so that any scheme is over, and in a unique way.
For the following definitions, we take as standard notation
to be a morphism of schemes. Parallel to the properties of schemes above, the following properties of morphisms are also of local nature, i.e. if there is an open covering of by some open subschemes, such that the restriction of to has the property, then has it, as well.
Read more about this topic: Glossary Of Scheme Theory
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