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Homotopy Theory of Schemes

Fabien Morel Mathematisches Institut der Universität München, München, Germany
Translated by James D. Lewis.
A co-publication of the AMS and the Société Mathématique de France
Available Formats:
Softcover ISBN: 978-0-8218-3164-9
Product Code: SMFAMS/12
List Price: $45.00 MAA Member Price:$40.50
AMS Member Price: $36.00 Click above image for expanded view Homotopy Theory of Schemes Fabien Morel Mathematisches Institut der Universität München, München, Germany Translated by James D. Lewis. A co-publication of the AMS and the Société Mathématique de France Available Formats:  Softcover ISBN: 978-0-8218-3164-9 Product Code: SMFAMS/12  List Price:$45.00 MAA Member Price: $40.50 AMS Member Price:$36.00
• Book Details

SMF/AMS Texts and Monographs
Volume: 122006; 104 pp
MSC: Primary 55; 13; 19;

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.

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

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

Mathematical Reviews
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Volume: 122006; 104 pp
MSC: Primary 55; 13; 19;

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.