Some comments on motivic nilpotence

Hornbostel, Jens

doi:10.1090/tran/7324

Some comments on motivic nilpotence
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by Jens Hornbostel; With an appendix by Marcus Zibrowius PDF

Trans. Amer. Math. Soc. 370 (2018), 3001-3015 Request permission

Abstract:

We discuss some results and conjectures related to the existence of the non-nilpotent motivic maps $\eta$ and $\mu _9$. To this purpose, we establish a theory of power operations for motivic $H_{\infty }$-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 $S[\eta ^{-1},\mu _9^{-1}]$ is closely related to higher Witt groups, where $S$ is the motivic sphere spectrum and $\eta$ and $\mu _9$ are explicit elements in $\pi _{**}(S)$.

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