Pub. Date:
Oxford University Press, USA
Categories of Commutative Algebras

Categories of Commutative Algebras

by Yves Diers, DiersYves Diers


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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 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. This innovative and original work will interest mathematicians in a range of specialities, including algebraists, categoricians, and algebraic geometers.

Product Details

ISBN-13: 9780198535867
Publisher: Oxford University Press, USA
Publication date: 07/02/1992
Pages: 288
Product dimensions: 6.31(w) x 9.50(h) x 0.88(d)

About the Author

Department de Mathematiques I.S.T.V Universite de Valenciennes F-59326 Valenciennes Cedex

Table of Contents

1. Zariski Categories
2. Classical Objects
3. Spectra
4. Schemes
5. Jacobson Ultraschemes
6. Algebraic Varieties
7. Zariski Toposes
8. Neat Objects and Morphisms
9. Flatness Properties
10. Etale Objects and Morphisms
11. Terminators
12. Some Constructions of Zariski Categories

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