The Stacks project

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

1. the scheme theoretic fibre of $f$ at $y \in Y$,

2. $f$ is a finite morphism,

3. a quasi-coherent $\mathcal{O}_ X$-module,

4. $X$ is variety,

5. $f$ is a smooth morphism,

6. $f$ is a proper morphism.