The eta-local motivic sphere
Bertrand J. Guillou, Daniel C. Isaksen
TL;DR
This paper computes the localized cohomology of the motivic Steenrod algebra over C and uses it to analyze the motivic stable homotopy groups of the eta-local motivic sphere, providing new insights into its structure.
Contribution
It introduces the computation of the h_1-localized cohomology of the motivic Steenrod algebra and applies it to the Adams spectral sequence for the eta-local motivic sphere, including some differentials.
Findings
Computed the h_1-localized cohomology of the motivic Steenrod algebra over C.
Determined some Adams differentials in the spectral sequence.
Formulated a conjecture about the remaining differentials.
Abstract
We compute the h_1-localized cohomology of the motivic Steenrod algebra over C. This serves as the input to an Adams spectral sequence that computes the motivic stable homotopy groups of the eta-local motivic sphere. We compute some of the Adams differentials, and we state a conjecture about the remaining differentials.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons