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 $X \to Y$.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).