On the zero slice of the sphere spectrum

2003/01/02 by Vladimir Voevodsky, Voevodsky, Vladimir
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #math.AG #math.AT

paper · pdf · doi:10.48550/arxiv.math/0301013

arxiv created 2003/01/02 · openalex publication_date 2003/01/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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