The motivic Adams spectral sequence

Dugger, Daniel¹ ; Isaksen, Daniel C²

¹ Department of Mathematics, University of Oregon, Eugene, OR 97403
² Department of Mathematics, Wayne State University, Detroit, MI 48202

Geometry & topology, Tome 14 (2010) no. 2, pp. 967-1014.

Résumé

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.

Détail

DOI : 10.2140/gt.2010.14.967

Keywords: motivic homotopy theory, Adams spectral sequence, May spectral sequence

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