Overview. Morphisms of Schemes [00AH]

    Definition 1. Ringed space [00AI]

      Definition 2. Morphism of sheaves [00AK]

        Definition 3. Morphism of ringed spaces [00AJ]

          A morphism of ringed spaces and is a continous map , together with a morphism of sheaves

          is the pushforward given by .

          Idea 4. Title [00AL]

            The idea with the is that we want to be able to pull back functions from to .

            • Morphisms of ringed spaces

            • Morphisms of locally ringed spaces

            • Morphisms of schemes

            • Morphisms to affine schemes

            • Morphisms from affine schemes

            • maps of graded rings and projective schmees

            • rational maps

            • open embeddings

            • quasi coherent quasi separated

            • affine and finite morphisms

            • Lying over Going up

            • Morphisms of (locally) finite type

            • Chevalley's Theorem