
Homotopy Theory of Schemes
Fabien Morel(Author)
American Mathematical Society (Publisher)
Will be published approx. on 30. October 2006
Book
Paperback/Softback
104 pages
978-0-8218-3164-9 (ISBN)
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Weight
210 gr
ISBN-13
978-0-8218-3164-9 (9780821831649)
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Schweitzer Classification
Content
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.