A Summary of the Lexicon.

In this chapter we give a brief summary of the algebra–geometry lexicon. All the statements we make here have been proved in Chap. 1 or 3, but for the sake of brevity we will not give any references. This lexicon really comes in two parts. The first links algebraic objects (such as affine algebras) to truly geometric objects (such as affine varieties). The second part is more general and links algebraic objects (such as rings) to objects that are geometric in a more abstract sense (such as spectra of rings). [ABSTRACT FROM AUTHOR]