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Homotopy Theory of Schemes
Fabien Morel, Mathematisches Institut der Universität München, Germany
Translated by James D. Lewis.
A co-publication of the AMS and Société Mathématique de France.

SMF/AMS Texts and Monographs
2006; 104 pp; softcover
Volume: 12
ISBN-10: 0-8218-3164-X
ISBN-13: 978-0-8218-3164-9
List Price: US$42
Member Price: US$33.60
Order Code: SMFAMS/12
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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 co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.


Graduate students and research mathematicians interested in algebraic geometry and algebraic topology.


"The translation should be of help to motivic homotopy theorists who read English more easily than French."

-- Mathematical Reviews

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