Exercise 111.59.1 (Definitions). Let $f : X \to Y$ be a morphism of schemes. Provide brief definitions of the italicized concepts.

the

*scheme theoretic fibre*of $f$ at $y \in Y$,$f$ is a

*finite morphism*,a

*quasi-coherent*$\mathcal{O}_ X$-module,$X$ is

*variety*,$f$ is a

*smooth morphism*,$f$ is a

*proper morphism*.

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