On the Zero Slice of the Sphere Spectrum

By Vladimir Voevodsky. 2003

53 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6ce560240ca5ce904a8a2a699340aba133673f50

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The generalized slices of Hermitian K‐theory (2016, background): “The rest of the proof essentially uses an argument of Voevodsky [ 28 , Section 4].”
Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, methodology): “1/ is the Eilenberg–MacLane spectrum MZ by the works of Levine [27] and Voevodsky [63].”
Motivic slices and coloured operads (2010, methodology): “Algebraic cobordism Voevodsky [32] has conjectured that the slices of the algebraic cobordism spectrum MGL are given by sqMGL = Σ2q,qMZ ⊗ MU2q.”
On the nonexistence of elements of Kervaire invariant one (2009, methodology): “MR MR2101286 (2005k:14042) [32] Vladimir Voevodsky, Open problems in the motivic stable homotopy theory.”
Motivic Eilenberg-MacLane spaces (2008, background): “Recall that for a linear representation ρ : G → Aut(V) of a finite group V we let Th(ρ) denote the quotient sheaf (in the Nisnevich topology) Th(ρ) = a+,Nis(V/V − {0}) where V and V − {0} are considered as representable sheaves on quasi-projective Gschemes (see [34]).”