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Interactions between Homotopy Theory and Algebra
Edited by: Luchezar L. Avramov, University of Nebraska-Lincoln, NE, J. Daniel Christensen, University of Western Ontario, London, Ontario, Canada, William G. Dwyer, University of Notre Dame, IN, Michael A. Mandell, Indiana University, Bloomington, IN, and Brooke E. Shipley, University of Illinois at Chicago, IL

Contemporary Mathematics
2007; 334 pp; softcover
Volume: 436
ISBN-10: 0-8218-3814-8
ISBN-13: 978-0-8218-3814-3
List Price: US$105
Member Price: US$84
Order Code: CONM/436
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This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.


Graduate students and research mathematicians interested in algebraic topology, commutative algebra, algebraic geometry and homological algebra.

Table of Contents

Introductory lecture series
  • P. Goerss and K. Schemmerhorn -- Model categories and simplicial methods
  • C. Huneke and A. Taylor -- Lectures on local cohomology
  • H. Krause -- Derived categories, resolutions, and Brown representability
  • H. Krause -- Exercises on derived categories, resolutions, and Brown representability
Topics lecture series
  • J. P. C. Greenlees -- Spectra for commutative algebraists
  • K. Hess -- Rational homotopy theory: A brief introduction
  • S. Iyengar -- André-Quillen homology of commutative algebras
  • W. G. Dwyer -- Local cohomology in commutative algebra, homotopy theory, and group cohomology
  • J. P. C. Greenlees -- First steps in brave new commutative algebra
  • M. Hovey -- Cotorsion pairs and model categories
  • K. Brüning and I. Burban -- Coherent sheaves on an elliptic curve
  • A. Adem -- Lectures on the cohomology of finite groups
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