Geodesic
On the Zero Slice of the Sphere Spectrum
Informatics and Automation, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 106-115

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We prove the motivic analogue of the statement saying that the zero stable homotopy group of spheres is $\mathbf Z$. In topology, this is equivalent to the fact that the fiber of the obvious map from the sphere $S^n$ to the Eilenberg–MacLane space $K(\mathbf Z,n)$ is $(n+1)$-connected. We prove our motivic analogue by an explicit geometric investigation of a similar map in the motivic world. Since we use the model of the motivic Eilenberg–MacLane spaces based on the symmetric powers, our proof works only in zero characteristic. 
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     author = {V. A. Voevodskii},
     title = {On the {Zero} {Slice} of the {Sphere} {Spectrum}},
     journal = {Informatics and Automation},
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     volume = {246},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2004_246_a6/}
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V. A. Voevodskii. On the Zero Slice of the Sphere Spectrum. Informatics and Automation, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 106-115. http://geodesic.mathdoc.fr/item/TRSPY_2004_246_a6/