The Stacks project

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

1. a scheme,

2. a morphism of schemes,

3. a quasi-coherent module on a scheme,

4. a variety over a field $k$,

5. a curve over a field $k$,

6. a finite morphism of schemes,

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

8. a dualizing sheaf on a scheme $X$ of dimension $d$ proper over a field $k$, and

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