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

the

*local ring of $X$ at a point $x$*,a

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

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

*affine open*of $X$,a

*finite morphism of schemes*$X \to Y$.

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