Volume 14, issue 2 (2010)

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The motivic Adams spectral sequence

Daniel Dugger and Daniel C Isaksen

Geometry & Topology 14 (2010) 967–1014
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
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