Triangulated categories
By: edited by Thorsten Holm, Peter Jørgensen, Raphaël Rouquier
Series: London Mathematical Society lecture note series
Publisher: Cambridge University Press
Published: 2010
Place of publication: Cambridge; New York
Language: eng
Number of pages: 463
ISBN-13: 9780521744317
Subjects: Triangulated categories
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 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"--Provided by publisher.

"This volume grew out of a Workshop on Triangulated Categories held at the University of Leeds in August 2006. The meeting, a Satellite of the International Congress of Mathematicians 2006, has been generously supported by the Leverhulme Foundation (via the network Algebras, Representations and Applications), the London Mathematical Society (Conference Grant Ref. 1438) and the University of Leeds. Over the past decades, triangulated categories have made their way into many different parts of mathematics, to the extent that today, they can be viewed as a unifying theory underlying major parts of modern mathematics. The Leeds workshop has brought together researchers from many parts of mathematics who all use triangulated methods but would not usually meet at more specialized conferences, with the aim to promote cross fertilization leading to new applications of triangulated categories. The present book collects surveys by leading experts reflecting a broad range of important topics covered at the workshop. However, it is not a proceedings volume recording precisely the talks given at the conference and it does not claim to be a comprehensive coverage of all the numerous applications of triangulated categories throughout mathematics"--Provided by publisher.
Notes: Includes bibliographical references.
Table of contents: title: Machine generated contents note: 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.