Categories of Commutative Algebras

by Yves Diers

Overview

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
Publication date:	07/02/1992
Pages:	280
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 Categories2. Classical Objects3. Spectra4. Schemes5. Jacobson Ultraschemes6. Algebraic Varieties7. Zariski Toposes8. Neat Objects and Morphisms9. Flatness Properties10. Etale Objects and Morphisms11. Terminators12. Some Constructions of Zariski Categories

Editorial Reviews

"A reader who delights in the categorical approach will find a great deal to interest him or her." —Mathematical Reviews

From the Publisher

A study of the properties and structures of categories of commutative algebras in order to bring out universal properties of these categories and provide a universal framework for commutative algebra and algebraic geometry. The aim is to extend the domain of validity and application of the large number of results obtained. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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