Motivic connective K-theories and the cohomology of A(1)

Details Motivic connective K-theories and the cohomology of A(1) Motivic connective K-theories and the cohomology of A(1)

2010-02-11

arxiv.org/abs/1002.2368v1

Mathematics

Algebraic Topology

Scientific paper

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also establish a theory of connective covers to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E_2-term of this spectral sequence involves Ext groups over the subalgebra A(1) of the motivic Steenrod algebra. We make several explicit computations of these E_2-terms in interesting special cases.

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