Marc Levine (1952-)
Philip Hirschhorn, A. Martsinkovsky, Alexandru Ion Suciu (1953-)-
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Arts and Sciences. Department of Mathematics.
Slice filtration, Motives, Motivic Atiyah-Hirzebruch Spectral Sequence
Motives (Mathematics), Homotopy theory
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 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.
Pelaez, Pablo, "Multiplicative properties of the slice filtration" (2008). Mathematics Dissertations. Paper 1. http://hdl.handle.net/2047/d1001617x
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