List questions from schemes

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List Question

Representability of transformations by morphisms

Universally closed morphism and closed morphism

Morphisms from a proper scheme to the affine line over a field must be constant.

Two definitions of Scheme theoretic image

Finite fiber- unramified morphisms

Is a nonzero divisor locally nonzero divisor?

Associated sheaf to a $\mathbb{C}$-module

pull-back and push-forward of quasi-coherent sheaves on affine schemes

Definition of algebraic variety

The $\mathbb C((z))$-rational points of a complex semi-simple group $G$

Example of an affine scheme where closed points aren't dense.

Source: Coherent locally free sheaves and projective modules

On a ringed space, show that the non vanishing set of $f$ is open, and that it is invertible there

Show that in a quasi-compact scheme every point has a closed point in its closure

Valuative criteria with varieties

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