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Homotopy Theory of Schemes (SMF/AMS Texts & Monographs)

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Home » Books » Science » Mathematics » Geometry » Algebraic

Homotopy Theory of Schemes

SMF/AMS Texts & Monographs

By Fabien Morel

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Format: Paperback, 104 pages
Published In: United States, 15 October 2006
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.

Table of Contents

Introduction The homotopic category Homotopic excision, homotopic purity and projective blow-ups Homotopic classification of vector bundles Appendix A: Review of homotopic algebra Appendix B: Ample families of invertible bundles on a scheme References.

EAN: 9780821831649
ISBN: 082183164X
Publisher: American Mathematical Society
Age Range: 15+ years
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