Let be a prime and , where is a prime different from . We show that the –completion of the stable homotopy group of spheres is a summand of the –completion of the motivic stable homotopy group of spheres over the finite field with elements, . With this, and assisted by computer calculations, we are able to explicitly compute the two-complete stable motivic stems for for all finite fields and and when assuming Morel’s connectivity theorem for holds.
"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