Homotopy Theory of Schemes
by
Fabien Morel
Book Details
Format
Paperback / Softback
Book Series
SMF/AMS Texts & Monographs
ISBN-10
082183164X
ISBN-13
9780821831649
Publisher
American Mathematical Society
Imprint
American Mathematical Society
Country of Manufacture
US
Country of Publication
GB
Publication Date
Oct 30th, 2006
Print length
104 Pages
Weight
212 grams
Dimensions
25.50 x 18.00 x 0.60 cms
Product Classification:
AlgebraGroups & group theoryGroups and group theoryAlgebraic topology
Ksh 7,400.00
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Presents a framework for applying the standard methods from homotopy theory to the category of smooth schemes over a base scheme $k$. This text 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.
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.
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