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.

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View Exercise 111.59.1 as pdf