Motivic Mahowald invariants over general base fields
Documenta mathematica, Tome 26 (2021), pp. 561-582.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The motivic Mahowald invariant was introduced in [\textit{J. D. Quigley}, Algebr. Geom. Topol. 19, No. 5, 2485--2534 (2019; Zbl 1436.55016)] and [\textit{J. D. Quigley}, J. Topol. 14, No. 2, 369--418 (2021; Zbl 07381853)] to study periodicity in the $\mathbb{C} $- and $\mathbb{R} $-motivic stable stems. In this paper, we define the motivic Mahowald invariant over any field $F$ of characteristic not two and use it to study periodicity in the $F$-motivic stable stems. In particular, we construct lifts of some of Adams' classical $v_1$-periodic families [\textit{J. F. Adams}, Topology 5, 21--71 (1966; Zbl 0145.19902)] and identify them as the motivic Mahowald invariants of powers of $2+\rho \eta $.
Classification : 14F42, 55P42, 55Q45, 55Q51
Keywords: motivic Mahowald invariant, root invariant, motivic periodicity, motivic stable stems
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     title = {Motivic {Mahowald} invariants over general base fields},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a42/}
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Quigley, J. D. Motivic Mahowald invariants over general base fields. Documenta mathematica, Tome 26 (2021), pp. 561-582. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a42/