Geometry & Topology

The motivic Adams spectral sequence

Daniel Dugger and Daniel C Isaksen

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732210

Digital Object Identifier
doi:10.2140/gt.2010.14.967

Mathematical Reviews number (MathSciNet)
MR2629898

Zentralblatt MATH identifier
1206.14041

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

Keywords
motivic homotopy theory Adams spectral sequence May spectral sequence

Citation

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. https://projecteuclid.org/euclid.gt/1513732210


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