# zbMATH — the first resource for mathematics

On the zero slice of the sphere spectrum. (English) Zbl 1182.14012
Proc. Steklov Inst. Math. 246, 93-102 (2004) and Tr. Mat. Inst. Steklova 246, 106-115 (2004).
Summary: We prove the motivic analogue of the statement saying that the zero stable homotopy group of spheres is $$\mathbb Z$$. 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 $$K(\mathbb Z,n)$$ 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.
For the entire collection see [Zbl 1087.14002].

##### MSC:
 14F42 Motivic cohomology; motivic homotopy theory 55P42 Stable homotopy theory, spectra
Full Text: