The Stacks project

Exercise 111.51.1 (Definitions). Provide definitions of the following concepts.

  1. $X$ is a scheme

  2. the morphism of schemes $f : X \to Y$ is finite

  3. the morphisms of schemes $f : X \to Y$ is of finite type

  4. the scheme $X$ is Noetherian

  5. the ${\mathcal O}_ X$-module ${\mathcal L}$ on the scheme $X$ is invertible

  6. the genus of a nonsingular projective curve over an algebraically closed field

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View Exercise 111.51.1 as pdf