Voevodsky, V. 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]. Cited in 1 ReviewCited in 14 Documents MSC: 14F42 Motivic cohomology; motivic homotopy theory 55P42 Stable homotopy theory, spectra PDF BibTeX XML Cite \textit{V. Voevodsky}, in: Algebraic geometry. Methods, relations, and applications. Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin. Moscow: Maik Nauka/Interperiodica. 93--102 (2004; Zbl 1182.14012) Full Text: MNR