Advisor(s)

Marc Levine (1952-)

Contributor(s)

Philip Hirschhorn, A. Martsinkovsky, Alexandru Ion Suciu (1953-)-

Date of Award

2008

Date Accepted

4-2008

Degree Grantor

Northeastern University

Degree Level

Ph.D.

Degree Name

Doctor of Philosophy

Department or Academic Unit

College of Arts and Sciences. Department of Mathematics.

Keywords

Slice filtration, Motives, Motivic Atiyah-Hirzebruch Spectral Sequence

Subject Categories

Motives (Mathematics), Homotopy theory

Disciplines

Mathematics

Abstract

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.

Document Type

Dissertation

Rights Holder

Pablo Pelaez


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