Schemes

Igor R. Shafarevich
Additional contact information
Igor R. Shafarevich: Steklov Mathematical Institute of the Russian Academy of Sciences, Algebra Section

Chapter Chapter 5 in Basic Algebraic Geometry 2, 2013, pp 3-47 from Springer

Abstract: Abstract The chapter introduces schemes as the new foundational object in algebraic geometry, with an extensive discussion of the ideas underlying this new notion. The prime spectrum SpecA of an arbitrary commutative ring with a 1 is defined as the set of prime ideals of A. It has a Zariski topology and a structure sheaf, a sheaf of rings with stalk at a point ${\frak{p}}$ the local ring $A_{{\frak{p}}}$ . Several examples are discussed, along with foundation notions, such as the dimension and product of affine schemes. General schemes are defined, together with the notion of product of schemes and the separatedness axiom in terms of closure of the diagonal.

Keywords: Prime Ideal; Algebraic Group; Local Ring; Maximal Ideal; Algebraic Variety (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-38010-5_1

Ordering information: This item can be ordered from
http://www.springer.com/9783642380105

DOI: 10.1007/978-3-642-38010-5_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().