Localization and Sheaves

1. Auflage 1995
ISBN: 978-0-582-27372-6
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 339, 256 Seiten, Format (B × H): 169 mm x 243 mm, Gewicht: 408 g

Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series

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.

Autoren/Hrsg.

Pascual, Jara

Vidal, Conchi

Verschoren, A

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

IntroductionGrothendieck categoriesTorsion in Grothendieck categoriesLocalization in Grothendieck categoriesGabriel filtersLocalization in module categoriesCompatibilityStabilityReflecting torsionThe relative Artin-Rees conditionRelative fully bounded ringsClassical localizationStructure sheavesFunctorial behaviourBibliographyIndex