Homotopy theory of schemes
Author(s)
Bibliographic Information
Homotopy theory of schemes
（SMF/AMS texts and monographs, v. 12）（Astérisque, no 256 (1999)）
American Mathematical Society , Société mathématique de France, c2006
- Other Title
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Théorie homotopique des schémas
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Note
Translation of: Théorie homotopique des schémas. Société mathématique de France. c1999
Bibliography: p. 103-104
Description and Table of Contents
Description
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.
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