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

Published online by Cambridge University Press:  24 May 2011

Daniel C. Isaksen  and
Armira Shkembi
Daniel C. Isaksen
Affiliation:
Department of Mathematics, Wayne State University, Detroit, MI 48202, USAisaksen@math.wayne.edu
Armira Shkembi
Affiliation:
Mathematics and Sciences Department, St. Leo University, St. Leo, FL 33574, USAarmira.shkembi@saintleo.edu
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Abstract

We make some computations in stable motivic homotopy theory over Spec ℂ, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct over ℂ a motivic analogue of the real K-theory spectrum KO. We also establish a theory of motivic connective covers over ℂ to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E2-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 E2-terms in interesting special cases.

Keywords

Motivic stable homotopy theoryAdams spectral sequenceconnective K-theorySteenrod algebra
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 3 , June 2011 , pp. 619 - 661
Copyright
Copyright © ISOPP 2011

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