This work applies Gabber's theorem on alterations to Voevodsky's work on mixed motives. We extend many fundamental theorems to DM(k, Z[1/p]) where p is the exponential characteristic of the perfect field k. Two applications are an isomorphism of Suslin that compares higher Chow …
"This work applies Gabber's theorem on alterations to Veovodsky's work on mixed motives ... Two applications are an isomorphism to Suslin that compares higher Chow groups and étale cohomology, and calculation of the motivic Steenrod algebra"--Back cover.
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…