Motivic Landweber exactness. (English) Zbl 1230.55005
Summary: We prove a motivic Landweber exact functor theorem. The main result shows the assignment given by a Landweber-type formula involving the 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.
MSC:
55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
55P42 | Stable homotopy theory, spectra |
14A20 | Generalizations (algebraic spaces, stacks) |
14F42 | Motivic cohomology; motivic homotopy theory |
19E08 | \(K\)-theory of schemes |