The motivic Adams spectral sequence

Dugger, Daniel; Isaksen, Daniel C

doi:10.2140/gt.2010.14.967

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The motivic Adams spectral sequence

Daniel Dugger and Daniel C Isaksen

Geometry & Topology 14 (2010) 967–1014

DOI: 10.2140/gt.2010.14.967

Abstract

We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field of characteristic $0$ . Our results are based on computer calculations and a motivic version of the May spectral sequence. We discuss features of the associated Adams spectral sequence and use these tools to give new proofs of some results in classical algebraic topology. We also consider a motivic Adams–Novikov spectral sequence. The investigations reveal the existence of some stable motivic homotopy classes that have no classical analogue.

Keywords

motivic homotopy theory, Adams spectral sequence, May spectral sequence

Mathematical Subject Classification 2000

Primary: 55T15, 14F42

References

Publication

Received: 5 February 2009

Accepted: 4 December 2009

Published: 31 March 2010

Proposed: Haynes Miller

Seconded: Bill Dwyer, Paul Goerss

Authors

Daniel Dugger
Department of Mathematics University of Oregon Eugene, OR 97403

Daniel C Isaksen
Department of Mathematics Wayne State University Detroit, MI 48202

Volume 14, issue 2 (2010)