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E-grāmata: Triangulated Categories

Edited by (University of Oxford), Edited by (University of Newcastle upon Tyne), Edited by
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"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 forgraduate 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 meetat 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.

Provided by publisher.

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

Papildus informācija

A 2010 collection of survey articles by leading experts on various aspects of triangulated categories.
Preface vii
Triangulated categories: definitions, properties, and examples
1(51)
Thorsten Holm
Peter Jorgensen
Cohomology over complete intersections via exterior algebras
52(24)
Luchezar L. Avramov
Srikanth B. Iyengar
Cluster algebras, quiver representations and triangulated categories
76(85)
Bernhard Keller
Localization theory for triangulated categories
161(75)
Henning Krause
Homological algebra in bivariant K-theory and other triangulated categories. I
236(54)
Ralf Meyer
Ryszard Nest
Derived categories and Grothendieck duality
290(61)
Amnon Neeman
Derived categories and algebraic geometry
351(20)
Raphael Rouquier
Triangulated categories for the analysts
371(18)
Pierre Schapira
Algebraic versus topological triangulated categories
389(19)
Stefan Schwede
Derived categories of coherent sheaves on algebraic varieties
408(44)
Yukinobu Toda
Rigid dualizing complexes via differential graded algebras (survey)
452
Amnon Yekutieli
Thorsten Holm is a Professor in the Faculty of Mathematics and Physics at Leibniz Universität Hannover. Peter Jųrgensen is Professor of Mathematics at Newcastle University. Raphaėl Rouquier is Waynflete Professor of Pure Mathematics in the Mathematical Institute at the University of Oxford.