Motivic Landweber exactness

  • Niko Naumann

  • Markus Spitzweck

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We prove a motivic Landweber exact functor theorem. The main result shows the assignment given by a Landweber-type formula involving the -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 -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.

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Niko Naumann, Markus Spitzweck, Motivic Landweber exactness. Doc. Math. 14 (2009), pp. 551–593

DOI 10.4171/DM/282