Some comments on motivic nilpotence

2015/11/23 by Hornbostel, Jens · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1511.07292

Abstract

We discuss some results and conjectures related to the existence of the non-nilpotent motivic maps η and μ₉. To this purpose, we establish a theory of power operations for motivic H_∞-spectra. Using this, we show that the naive motivic analogue of the unstable Kahn-Priddy theorem fails. Over the complex numbers, we show that the motivic T-spectrum S[η^-1,μ₉^-1] is closely related to higher Witt groups, where S is the motivic sphere spectrum and η, σ and μ₉ are explicit elements in π_**(S).

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• Motivic Homotopy Groups of Spheres and Free Summands of Stably Free Modules

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