Geometry & Topology

The motivic Adams spectral sequence

Daniel Dugger and Daniel C Isaksen

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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.

Article information

Geom. Topol., Volume 14, Number 2 (2010), 967-1014.

Received: 5 February 2009
Accepted: 4 December 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55T15: Adams spectral sequences 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15]

motivic homotopy theory Adams spectral sequence May spectral sequence


Dugger, Daniel; Isaksen, Daniel C. The motivic Adams spectral sequence. Geom. Topol. 14 (2010), no. 2, 967--1014. doi:10.2140/gt.2010.14.967.

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