DOCUMENTA MATHEMATICA, Vol. 14 (2009), 551-593

Niko Naumann, Markus Spitzweck, Paul Arne Østvær

Motivic Landweber Exactness

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.

2000 Mathematics Subject Classification: 55N22, 55P42, 14A20, 14F42, 19E08.

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