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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
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