In the current chapter, we will define the notion of scheme. In a sense, the remainder of this book is devoted to the study of schemes, so this notion is fundamental for all which follows. Schemes arise by “gluing affine schemes”, similarly as prevarieties are obtained by gluing affine varieties. Therefore after the preparations in the previous chapter, the definition is very simple, see (3.1). As for varieties we define projective space (3.6) by gluing copies of affine spaces. This is an example of a scheme which is not affine.
KeywordsOpen Subset Topological Space Prime Ideal Irreducible Component Local Ring
Unable to display preview. Download preview PDF.