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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.

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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