Categories of commutative algebras
著者
書誌事項
Categories of commutative algebras
（Oxford science publications）
Clarendon press , Oxford University Press, 1992
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注記
Bibliography: p. [265]-266
Includes indexes
内容説明・目次
内容説明
This book studies the universal constructions and properties in categories of commutative algebras, bringing out the specific properties that make commutative algebra and algebraic geometry work. Two new universal constructions are presented and used here for the first time. The author shows that the concepts and constructions arising in commutative algebra and algebraic geometry are not bound so tightly to the absolute universe of rings, but possess a universality
that is independent of them and can be interpreted in various categories of discourse. This brings new flexibility to classical commutative algebra and affords the possibility of extending the domain of validity and the application of the vast number of results obtained in classical commutative
algebra.
目次
- Introduction
- Zariski categories
- Classical objects
- Spectra
- Schemes
- Jacobson ultraschemes
- Algebraic varieties
- Zariski toposes
- Neat objects and morphisms
- Flatness properties
- Etale objects and morphisms
- Terminators
- Some constructions of Zariski categories.
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