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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
Homotopy Theory of Schemes
Softcover ISBN:  978-0-8218-3164-9
Product Code:  SMFAMS/12
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
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
Softcover ISBN:  978-0-8218-3164-9
Product Code:  SMFAMS/12
List Price: $48.00
MAA Member Price: $43.20
AMS Member Price: $38.40
  • 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.

    Titles in this series are co-published 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
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.

Titles in this series are co-published 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.

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

    Mathematical Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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