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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.
Introductory lecture series: Model categories and simplicial methods by P. Goerss and K. Schemmerhorn Lectures on local cohomology by C. Huneke and A. Taylor Derived categories, resolutions, and Brown representability by H. Krause Exercises on derived categories, resolutions, and Brown representability by H. Krause Topics lecture series: Spectra for commutative algebraists by J. P. C. Greenless Rational homotopy theory: A brief introduction by K. Hess Andre-Quillen homology of commutative algebras by S. Iyengar Local cohomology in commutative algebra, homotopy theory, and group cohomology by W. G. Dwyer First steps in brave new commutative algebra by J. P. C. Greenless Cotorsion pairs and model categories by M. Hovey Coherent sheaves on an elliptic curve by K. Bruning and I. Burban Lectures on the cohomology of finite groups by A. Adem.
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- ID: 9780821838143
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