Topology Seminar: A model for Motivic stable homotopy in classical homotopy

Morel-Voevodsky's motivic stable category of schemes plays a crutial role in today's stable homotopy. For instance, a recent work of Isaksen-Wang push our knowledge of stable stems up to dimension 93. In this joint work with Achim Krause and Bogdan Gheorghe, we construct a new model category, equivalent to the cellular motivic stable category, but whose construction lies entierly in the realm of classical stable homotopy theory. Moreover, this construction emphasizes the close relationship between cellular motivic homotopy theory and the theory of BP-resolutions. If time permits, I will talk about a new computation of the motivic dual Steenrod algebra using this new model, as well as the perspectives opened by similar constructions.