Triangulated Categories

A 2010 collection of survey articles by leading experts on various aspects of triangulated categories.

Thorsten Holm (Edited by), Peter Jørgensen (Edited by), Raphaël Rouquier (Edited by)

9780521744317, Cambridge University Press

Paperback, published 24 June 2010

472 pages
22.6 x 15 x 2.5 cm, 0.69 kg

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.

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.

Subject Areas: Algebra [PBF]