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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].

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