ISBN 9780582273726,Localization And Sheaves

Localization And Sheaves

Publisher:

Taylor & Francis

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ISBN 9780582273726
Publisher

Taylor & Francis

Publication Year 2014
ISBN-13

ISBN 9780582273726

ISBN-10 0582273722
Binding

Hardback

Number of Pages 256 Pages
Language (English)
Subject

Literature fiction

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.

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