A01=Fabien Morel
Author_Fabien Morel
Category=PBF
Category=PBG
Category=PBPD
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Product details
- ISBN 9780821831649
- Weight: 210g
- Publication Date: 30 Oct 2006
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
