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The Stacks project

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

  1. a scheme,

  2. a quasi-coherent module on a scheme X,

  3. a flat morphism of schemes X \to Y,

  4. a finite morphism of schemes X \to Y,

  5. a group scheme G over a base scheme S,

  6. a family of varieties over a base scheme S,

  7. the degree of a closed point x on a variety X over the field k,

  8. the usual logarithmic height of a point p = (a_0 : \ldots : a_ n) in \mathbf{P}^ n(\mathbf{Q}), and

  9. a C_ i field.


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