#### DOCUMENTA MATHEMATICA, Vol. 18 (2013), 51-70

Pablo Pelaez

Birational Motivic Homotopy Theories and the Slice Filtration

We show that there is an equivalence of categories between the orthogonal components for the slice filtration and the birational motivic stable homotopy categories which are constructed in this paper. Relying on this equivalence, we are able to describe the slices for projective spaces (including $\ P ^{\infty}$), Thom spaces and blow ups.

2010 Mathematics Subject Classification: 14F42

Keywords and Phrases: Birational Invariants, Motivic Homotopy Theory, Motivic Spectral Sequence, Slice Filtration.

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