On the zero slice of the sphere spectrum

Abstract

In this paper we prove over fields of characteristic zero that the zero slice of the motivic sphere spectrum is the motivic Eilenberg-Maclane spectrum. As a corollary one concludes that the slices of any spectrum are modules over the motivic Eilenberg-MacLane spectrum. To prove our result we analyze the unstable homotopy type of the symmetric powers of the T-sphere.

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