Exercise 111.65.1 (Definitions). Provide brief definitions of the italicized concepts.

a

*scheme*,a

*quasi-coherent module*on a scheme $X$,a

*flat*morphism of schemes $X \to Y$,a

*finite*morphism of schemes $X \to Y$,a

*group scheme*$G$ over a base scheme $S$,a

*family of varieties*over a base scheme $S$,the

*degree*of a closed point $x$ on a variety $X$ over the field $k$,the usual

*logarithmic height*of a point $p = (a_0 : \ldots : a_ n)$ in $\mathbf{P}^ n(\mathbf{Q})$, anda

*$C_ i$ field*.

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