Naumann, Niko; Spitzweck, Markus

Motivic Landweber exactness

Doc. Math., J. DMV 14, 551-593 (2009)


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.

Mathematics Subject Classification

55N22, 55P42, 14A20, 14F42, 19E08