Multiplicative Properties of the Slice Filtration

Details Multiplicative Properties of the Slice Filtration Multiplicative Properties of the Slice Filtration

2008-06-10

arxiv.org/abs/0806.1704v3

Mathematics

Algebraic Geometry

bibliography corrected, proof of former lemma 3.5.60 corrected

Scientific paper

We show that the slice filtration introduced by Voevodsky is compatible in a suitable sense with the symmetric monoidal structure in the category of motivic symmetric T-spectra constructed by Jardine. It follows from this compatibility that the zero slice of the sphere spectrum s_{0}(1) is a ring spectrum and that for every symmetric T-spectrum X, and every integer n; the n-slice s_{n}(X) is a module over s_{0}(1). In particular, if the base scheme is a field of characteristic zero, we have that all the slices s_{n}(X) are big motives in the sense of Voevodsky. We also get as a corollary that the smash product of symmetric T-spectra induces pairings in the motivic Atiyah-Hirzebruch spectral sequence.

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