Localization and Sheaves: A Relative Point of View (Chapman & Hall/CRC Research Notes in Mathematics Series)

Pascual, Jara; Vidal, Conchi; Verschoren, A

ISBN 10: 0582273722 / ISBN 13: 9780582273726

Published by Chapman and Hall/CRC, 1995

About this Item

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Bibliographic Details

• Title: Localization and Sheaves: A Relative Point of View (Chapman & Hall/CRC Research Notes in Mathematics Series)
• Publisher: Chapman and Hall/CRC
• Publication Date: 1995
• Language: English
• ISBN 10: 0582273722
• ISBN 13: 9780582273726
• Binding: Soft cover
• Condition: good

About this title

Synopsis

This book completely solves the problem of representing rings (and modules over them), which are locally noetherian over subsets of their prime spectrum by structure sheaves over this subset. In order to realise this, one has to develop the necessary localization theory as well as to study local equivalents of familiar concepts like the Artin-Rees property, Ore sets and the second layer condition. The first part of the book is introductory and self-contained, and might serve as a starting course (at graduate level) on localization theory within Grothendieck categories. The second part is more specialised and provides the basic machinery needed to effectively these structure sheaves, as well as to study their functorial behaviour. In this way, the book should be viewed as a first introduction to what should be called relative noncommutative algebraic geometry.