Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. These self-contained articles are a useful introduction for graduate students entering the field and a valuable reference for experts.
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises; Printed music items
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 28 mm
Gewicht
ISBN-13
978-0-521-74431-7 (9780521744317)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Thorsten Holm is a Professor in the Faculty of Mathematics and Physics at Leibniz Universitaet Hannover. Peter Jorgensen is Professor of Mathematics at Newcastle University. Raphael Rouquier is Waynflete Professor of Pure Mathematics in the Mathematical Institute at the University of Oxford.
Herausgeber*in
University of Newcastle upon Tyne
University of Oxford
Preface; Introduction; 1. Cohomology over complete intersections via exterior algebras Luchezar Avramov and Srikanth Iyengar; 2. Cluster algebras, quiver representations and triangulated categories Bernhard Keller; 3. Localization for triangulated categories Henning Krause; 4. Homological algebra in bivariant K-theory and other triangulated categories Ralf Meyer and Ryszard Nest; 5. Derived categories and Grothendieck duality Amnon Neeman; 6. Algebraic versus topological triangulated categories Stefan Schwede; 7. Derived categories and algebraic geometry Raphael Rouquier; 8. Triangulated categories for the analysts Pierre Schapira; 9. Derived categories of coherent sheaves on algebraic varieties Yukinobu Toda; 10. Rigid dualizing complexes via differential graded algebras Amnon Yekutieli.
