schemes – Konrad Voelkel's Blog – Mathemagically

A closed immersion is finite. A finite morphism is proper, affine and of finite type. Finite morphisms are separated. Open immersions are etale, therefore smooth, thus flat; open immersions are separated. Quasi-compact and locally of finite type implies of finite type. Projective and quasi-finite is the same as finite. Proper morphisms are universally closed. Flat morphisms of finite type are universally open.

What is a flat module? I give the definition, examples and counter-examples, some properties and many useful exercises.

As I'm currently reading Voevodskys paper on A¹-homotopy theory of schemes, I will by and by write a little "walk-through" with hints & comments on how to find additional information to better (or even start to) understand the paper.