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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Condition: New. 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. Series: SMF/AMS Texts & Monographs. Num Pages: 104 pages. BIC Classification: PBF; PBG; PBPD. Category: (P) Professional & Vocational. Dimension: 255 x 180 x 6. Weight in Grams: 212. . 2006. Paperback. . . . . Seller Inventory # V9780821831649
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Condition: New. 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. Series: SMF/AMS Texts & Monographs. Num Pages: 104 pages. BIC Classification: PBF; PBG; PBPD. Category: (P) Professional & Vocational. Dimension: 255 x 180 x 6. Weight in Grams: 212. . 2006. Paperback. . . . . Books ship from the US and Ireland. Seller Inventory # V9780821831649
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