Geodesic
The motivic Mahowald invariant
Quigley, J D1
1 Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States, Department of Mathematics, Cornell University, Ithaca, NY, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2485-2534

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

The classical Mahowald invariant is a method for producing nonzero classes in the stable homotopy groups of spheres from classes in lower stems. We study the Mahowald invariant in the setting of motivic stable homotopy theory over Spec(ℂ). We compute a motivic version of the C2–Tate construction for various motivic spectra, and show that this construction produces “blueshift” in these cases. We use these computations to show that for i ≥ 1, the Mahowald invariant of ηi is the first element in Adams filtration i of the w1–periodic families constructed by Andrews (2018). This provides an exotic periodic analog of the computation of Mahowald and Ravenel (1993) that for i ≥ 1, the classical Mahowald invariant of 2i, is the first element in Adams filtration i of the v1–periodic families constructed by Adams (1966).

DOI : 10.2140/agt.2019.19.2485
Classification : 55P42
Keywords: Mahowald invariant, root invariant, motivic $v_1$–periodicity, motivic $w_1$–periodicity, motivic Tate construction

Quigley, J D 1

1 Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States, Department of Mathematics, Cornell University, Ithaca, NY, United States 
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Quigley, J D. The motivic Mahowald invariant. Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2485-2534. doi: 10.2140/agt.2019.19.2485

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