Motivic Landweber exactness

Abstract

We prove a motivic Landweber exact functor theorem. The main result shows the assignment given by a Landweber-type formula involving the $\mathsf{MGL}$-homology of a motivic spectrum defines a homology theory on the motivic stable homotopy category which is representable by a Tate spectrum. Using a universal coefficient spectral sequence we deduce formulas for operations of certain motivic Landweber exact spectra including homotopy algebraic $K$-theory. Finally we employ a Chern character between motivic spectra in order to compute rational algebraic cobordism groups over fields in terms of rational motivic cohomology groups and the Lazard ring.