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New families in the homotopy of the motivic sphere spectrum


Author: Michael J. Andrews
Journal: Proc. Amer. Math. Soc. 146 (2018), 2711-2722
MSC (2010): Primary 55Q45, 55Q51, 55T15, 14F42
DOI: https://doi.org/10.1090/proc/13940
Published electronically: February 16, 2018
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Abstract: Using iterates of the Adams self map $ v_1^4:\Sigma ^8 S/2\to S/2$ one can construct infinite families of elements in the stable homotopy groups of spheres, the $ v_1$-periodic elements of order $ 2$. In this paper we work motivically over $ \mathbb{C}$ and construct a non-nilpotent self map $ w_1^4:\Sigma ^{20,12}S/\eta \to S/\eta $. We then construct some infinite families of elements in the homotopy of the motivic sphere spectrum, $ w_1$-periodic elements killed by $ \eta $.


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Additional Information

Michael J. Andrews
Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555
Email: mjandr@math.ucla.edu

DOI: https://doi.org/10.1090/proc/13940
Keywords: Non-nilpotent self map, motivic self map, motivic Adams-Novikov spectral sequence.
Received by editor(s): June 29, 2017
Received by editor(s) in revised form: August 20, 2017
Published electronically: February 16, 2018
Dedicated: Dedicated to the memory of Amelia Perry.
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2018 American Mathematical Society

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