New families in the homotopy of the motivic sphere spectrum

Andrews, Michael

doi:10.1090/proc/13940

New families in the homotopy of the motivic sphere spectrum
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Proc. Amer. Math. Soc. 146 (2018), 2711-2722 Request permission

Abstract:

Using iterates of the Adams self map $v_1^4:\Sigma ^8 S/2\longrightarrow S/2$ 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 $w_1^4:\Sigma ^{20,12}S/\eta \longrightarrow S/\eta$. 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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