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2017 Two-complete stable motivic stems over finite fields
Glen Matthew Wilson, Paul Østvær
Algebr. Geom. Topol. 17(2): 1059-1104 (2017). DOI: 10.2140/agt.2017.17.1059

Abstract

Let be a prime and q = pν, where p is a prime different from . We show that the –completion of the nth stable homotopy group of spheres is a summand of the –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.

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Glen Matthew Wilson. Paul Østvær. "Two-complete stable motivic stems over finite fields." Algebr. Geom. Topol. 17 (2) 1059 - 1104, 2017. https://doi.org/10.2140/agt.2017.17.1059

Information

Received: 2 February 2016; Revised: 3 October 2016; Accepted: 12 October 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1361.14020
MathSciNet: MR3623682
Digital Object Identifier: 10.2140/agt.2017.17.1059

Subjects:
Primary: 14F42, 16-04, 18G15, 55T15

Rights: Copyright © 2017 Mathematical Sciences Publishers

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