Triangulated Categories

Erscheinungsjahr 2012
ISBN: 978-0-521-74431-7
Verlag: Cambridge University Press

Buch, Englisch, Band 375, 472 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 760 g

Reihe: London Mathematical Society Lecture Note Series

• Ideal reference for mathematicians interested in modern aspects of triangulated categories
• Explores applications from very different areas of mathematics
• A suitable introduction to the subject for graduate students
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 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.

Autoren/Hrsg.

Holm, Thorsten

Jørgensen, Peter

Rouquier, Raphaël

Fachgebiete

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

Inhaltsverzeichnis

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 Raphaël 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.

Über Autor(innen)

Jørgensen, Peter
Peter Jørgensen is Professor of Mathematics at Newcastle University.

Holm, Thorsten
Thorsten Holm is a Professor in the Faculty of Mathematics and Physics at Leibniz Universität Hannover.

Rouquier, Raphaël
Raphaël Rouquier is Waynflete Professor of Pure Mathematics in the Mathematical Institute at the University of Oxford.