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 $\pi _{**}(S)$.References
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Additional Information
- Jens Hornbostel
- Affiliation: Fachgruppe Mathematik und Informatik, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
- MR Author ID: 653668
- Email: hornbostel@math.uni-wuppertal.de
- Marcus Zibrowius
- Affiliation: Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitäts- straße 1, 40225 Düsseldorf, Germany
- MR Author ID: 946630
- Email: marcus.zibrowius@uni-duesseldorf.de
- Received by editor(s): September 22, 2016
- Received by editor(s) in revised form: January 24, 2017, and June 26, 2017
- Published electronically: December 19, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 3001-3015
- MSC (2010): Primary 14F42; Secondary 19G12, 19G38, 55P43
- DOI: https://doi.org/10.1090/tran/7324
- MathSciNet review: 3748592