The motivic adams spectral sequence

By Daniel Dugger, Daniel Isaksen. 2009

98 citations recorded by the source corpus.

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. 55T15, 14F42

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d6eeb27dd82250e677b8902d48358a26e2a145fc

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Citations in the corpus

Low-dimensional Milnor–Witt stems over ℝ (2015, methodology): “The motivic May spectral sequence [3] has E1-page generated by classes hij , and converges to Ext .”
The motivic Steenrod algebra in positive characteristic (2013, background): “r any motivic spectrum Eover S, MZ/ℓ∗∗Eis a left comodule over the dual motivic Steenrod algebra A∗∗. This fact is essential for adapting Adams spectral sequence techniques to motivic homotopy theory [DI10], [HKO11]. Secondly, we generalize the main result of [RØ08] by showing that Voevodsky’s categ”
Stable Stems (2014, methodology): “See also [13] for a different proof of Lemma 2.”
A comparison of motivic and classical stable homotopy theories (2011, methodology): “Dugger and Isaksen [7] and independently Hu, Kriz and Ormsby [14] have constructed motivic versions of the Adams and Adams–Novikov spectral sequences, and have made explicit computations.”