Geodesic
On the Zero Slice of the Sphere Spectrum
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 106-115.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2004_246_a6,
     author = {V. A. Voevodskii},
     title = {On the {Zero} {Slice} of the {Sphere} {Spectrum}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {106--115},
     publisher = {mathdoc},
     volume = {246},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_246_a6/}
}
TY  - JOUR
AU  - V. A. Voevodskii
TI  - On the Zero Slice of the Sphere Spectrum
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 106
EP  - 115
VL  - 246
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2004_246_a6/
LA  - en
ID  - TM_2004_246_a6
ER  - 
%0 Journal Article
%A V. A. Voevodskii
%T On the Zero Slice of the Sphere Spectrum
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 106-115
%V 246
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2004_246_a6/
%G en
%F TM_2004_246_a6
V. A. Voevodskii. On the Zero Slice of the Sphere Spectrum. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 106-115. http://geodesic.mathdoc.fr/item/TM_2004_246_a6/

[1] Dold A., Lashof R., “Principal quasi-fibrations and fiber homotopy equivalence of bundles”, Ill. J. Math., 3 (1959), 285–305 | MR | Zbl

[2] Voevodsky V., Lectures on motivic cohomology 2000/2001, written by Pierre Deligne, 2000/2001

[3] Voevodsky V., “Open problems in the motivic stable homotopy theory, I”, Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), Int. Press Lect. Ser., 3, Int. Press, Somerville, MA, 2002, 3–34 | MR | Zbl

[4] Suslin A., Voevodsky V., “Singular homology of abstract algebraic varieties”, Invent. Math., 123:1 (1996), 61–94 | DOI | MR | Zbl