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Some comments on motivic nilpotence


Author: Jens Hornbostel; With an appendix by Marcus Zibrowius
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
Published electronically: December 19, 2017
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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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Additional Information

Jens Hornbostel
Affiliation: Fachgruppe Mathematik und Informatik, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
Email: hornbostel@math.uni-wuppertal.de

Marcus Zibrowius
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitäts- straße 1, 40225 Düsseldorf, Germany
Email: marcus.zibrowius@uni-duesseldorf.de

DOI: https://doi.org/10.1090/tran/7324
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
Article copyright: © Copyright 2017 American Mathematical Society

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