Dieudonne

#4.64 Geometric point and geometry fibre (over a fixed geometric point)

Fibre, generic fibre (over an irreducible scheme) and special fibre (over Spec of a DVR)

#61 Spec k(x) to X

notice Speck(x) to Spec O_X,x is a closed immersion: the unique point is mapped to maximal ideal, as in the level of algebra, the inverse image of (0) in k(x) is that maximal ideal

SpecOXx to X, a canonical map

SpecOXx to X, a canonical map

section vs k-rational points vs "real" points

#4.58 Separated scheme (cf. 4.49)

#4.57 Étale morphism

#4.56 Flat morphism

#4.55 Normal ring (=integral closed); normal scheme