Localization and Sheaves : A Relative Point of View book cover
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Localization and Sheaves
A Relative Point of View



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ISBN 9780582273726
Published November 30, 1995 by Chapman and Hall/CRC
256 Pages

 
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Book Description

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.

Table of Contents

Introduction
Grothendieck categories
Torsion in Grothendieck categories
Localization in Grothendieck categories
Gabriel filters
Localization in module categories
Compatibility
Stability
Reflecting torsion
The relative Artin-Rees condition
Relative fully bounded rings
Classical localization
Structure sheaves
Functorial behaviour
Bibliography
Index

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