Let ℓ be a prime and q = pυ, 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.

Two-complete stable motivic stems over finite fields / G.M. Wilson, P.A. Oestvaer. - In: ALGEBRAIC AND GEOMETRIC TOPOLOGY. - ISSN 1472-2739. - 17:2(2017), pp. 1059-1104. [10.2140/agt.2017.17.1059]

Two-complete stable motivic stems over finite fields

P.A. Oestvaer
2017

Abstract

Let ℓ be a prime and q = pυ, 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.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/860120
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