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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
Front Cover for Homotopy Theory of Schemes
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
Front Cover for Homotopy Theory of Schemes
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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
  • 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.

    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
  • Request Review Copy
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.

Readership

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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