Homotopy Theory of Schemes

Homotopy Theory of Schemes
Author :
Publisher : American Mathematical Soc.
Total Pages : 116
Release :
ISBN-10 : 082183164X
ISBN-13 : 9780821831649
Rating : 4/5 (4X Downloads)

Book Synopsis Homotopy Theory of Schemes by : Fabien Morel

Download or read book Homotopy Theory of Schemes written by Fabien Morel and published by American Mathematical Soc.. This book was released on 2006 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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