Triangulated Categories (London Mathematical Society Lecture Note Series)

Holm, Thorsten (EDT)/ Jørgensen, Peter (EDT)/ Rouquier, Raphaël (EDT)

Cambridge University Press（2010/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 472 p.
• 言語 ENG
• 商品コード 9780521744317
• DDC分類 512.55

Full Description

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.

Contents

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.