Categories of Commutative Algebras

Erscheinungsjahr 1992
ISBN: 978-0-19-853586-7
Verlag: OUP Oxford

Buch, Englisch, 280 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 615 g

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.

Autoren/Hrsg.

Diers, Yves

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.