A comparison of motivic and classical stable homotopy theories (Q2928214)

This paper establishes an equivalences between two homotopy theories, one the Nisnevich local homotopy theory of smooth schemes over a field \(k\) of characteristic zero, and a homotopy theory of smooth compactifications. A motivation comes from generalizations of Deligne-Beilinson cohomology using homotopical methods, which require the steps of the Hodge filtration on singular cohomology of complex varieties to be representable. Representability follows from the equivalence of homotopy theories established in this paper.