Two-complete stable motivic stems over finite fields

Wilson, Glen Matthew¹ ; Østvær, Paul¹

¹Department of Mathematics, University of Oslo, PO Box 1053, 0316 Oslo, Norway

Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 1059-1104

Résumé

Let ℓ be a prime and q = pν, where p is a prime different from ℓ. We show that the ℓ–completion of the nth stable homotopy group of spheres is a summand of the ℓ–completion of the (n,0) motivic stable homotopy group of spheres over the finite field with q elements, Fq. With this, and assisted by computer calculations, we are able to explicitly compute the two-complete stable motivic stems πn,0(Fq)2 ∧ for 0 ≤ n ≤ 18 for all finite fields and π19,0(Fq)2 ∧ and π20,0(Fq)2 ∧ when q ≡ 1 mod 4 assuming Morel’s connectivity theorem for Fq holds.

Détail

DOI : 10.2140/agt.2017.17.1059

Classification : 16-04, 14F42, 18G15, 55T15
Keywords: motivic Adams spectral sequence, stable motivic stems over finite fields, computer-assisted motivic Ext group calculations

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