Localization and Sheaves: A Relative Point of View, 1st Edition (Hardback) book cover

Localization and Sheaves

A Relative Point of View, 1st Edition

By Jara Pascual, Conchi Vidal, A Verschoren

Chapman and Hall/CRC

256 pages

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Hardback: 9780582273726
pub: 1995-11-30
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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


Grothendieck categories

Torsion in Grothendieck categories

Localization in Grothendieck categories

Gabriel filters

Localization in module categories



Reflecting torsion

The relative Artin-Rees condition

Relative fully bounded rings

Classical localization

Structure sheaves

Functorial behaviour



About the Series

Chapman & Hall/CRC Research Notes in Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Number Theory