Exercise 111.63.1 (Definitions). Provide brief definitions of the italicized concepts.

a

*scheme*,a

*morphism of schemes*,a

*quasi-coherent module*on a scheme,a

*variety*over a field $k$,a

*curve*over a field $k$,a

*finite morphism*of schemes,the

*cohomology*of a sheaf of abelian groups $\mathcal{F}$ over a topological space $X$,a

*dualizing sheaf*on a scheme $X$ of dimension $d$ proper over a field $k$, anda

*rational map*from a variety $X$ to a variety $Y$.

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