The Stacks project

Exercise 109.57.1 (Definitions). Let $(X, \mathcal{O}_ X)$ be a scheme. Provide definitions of the italicized concepts.

  1. the local ring of $X$ at a point $x$,

  2. a quasi-coherent sheaf of $\mathcal{O}_ X$-modules,

  3. a coherent sheaf of $\mathcal{O}_ X$-modules (please assume $X$ is locally Noetherian,

  4. an affine open of $X$,

  5. a finite morphism of schemes $X \to Y$.

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