What is algebraic geometry
What is algebraic geometry? I am just giving a summary of the usual pipeline of algebraic geometry. We start from the scheme theory and then develop the quasi-coherent sheaf theory and then study various type of scheme and their morphism. Then we can study the blows up and pullback etc. We also study some of the projective geometry and projective scheme. Spec versus Proj constructions: (Affine schemes) Given a ring A and an A -module M : We get an affine scheme X = Spec A and a quasi-coherent O X -module M ~ . For any p ∈ Spec A and any f ∈ A we have M ~ p ≅ M p and Γ ( D ( f ) , M ~ ) ≅ M f . In particular Γ ( X , M ~ ) ≅ M . ...