Homotopy Theory of Schemes - Morel, Fabien

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.