Motivic Landweber exactness

By N. Axel Naumann, P. Ostvaer, Markus Spitzweck. Documenta Mathematica, 2008

76 citations recorded by the source corpus.

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 spec- tral sequence we deduce formulas for operations of certain motivic Landweber exact spectra including homotopy algebraic K-theory. Fi- nally 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1742d05fffb2b65c30158674a080f700237ebd8d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the motivic spectra representing algebraic cobordism and algebraic $K$-theory (2007, methodology): “See [21] for the motivic analogue of Landweber exactness.”
The C2–spectrum Tmf1(3) and its invertible modules (2015, background): “Part (a) of it can be proven analogously to Landweber exactness in the motivic setting as in [55], though we follow their approach only loosely.”
Triangulated Categories of Mixed Motives (2009, methodology): “In particular, this shows that HB is canonically isomorphic to the spectrum denoted by LQ in [NSØ08], which corresponds to the universal additive formal group law over Q.”