Volume 17, issue 2 (2017)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Two-complete stable motivic stems over finite fields

Glen Matthew Wilson and Paul Arne Østvær

Algebraic & Geometric Topology 17 (2017) 1059–1104
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.

Keywords
motivic Adams spectral sequence, stable motivic stems over finite fields, computer-assisted motivic Ext group calculations
Mathematical Subject Classification 2010
Primary: 16-04, 14F42, 18G15, 55T15
References
Publication
Received: 2 February 2016
Revised: 3 October 2016
Accepted: 12 October 2016
Published: 14 March 2017
Authors
Glen Matthew Wilson
Department of Mathematics
University of Oslo
PO Box 1053
0316 Oslo
Norway
Paul Arne Østvær
Department of Mathematics
University of Oslo
PO Box 1053
0316 Oslo
Norway