
Introduction  Table of Contents  Supplementary Material 
SMF/AMS Texts and Monographs 2006; 104 pp; softcover Volume: 12 ISBN10: 082183164X ISBN13: 9780821831649 List Price: US$42 Member Price: US$33.60 Order Code: SMFAMS/12 See also: Residues and Duality for Projective Algebraic Varieties  Ernst Kunz, David A Cox and Alicia Dickenstein  In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme \(k\). He defines the homotopy category \(h(\mathcal{E}_k)\) of smooth \(k\)schemes and shows that it plays the same role for smooth \(k\)schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic \(K\)theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry. Titles in this series are copublished with Société Mathématique de France. SMF members are entitled to AMS member discounts. Readership Graduate students and research mathematicians interested in algebraic geometry and algebraic topology. Reviews "The translation should be of help to motivic homotopy theorists who read English more easily than French."  Mathematical Reviews 


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