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The unstable slice filtration

Author: Pablo Pelaez
Journal: Trans. Amer. Math. Soc. 366 (2014), 5991-6025
MSC (2010): Primary 14F42
Published electronically: May 22, 2014
MathSciNet review: 3256191
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Abstract: The main goal of this paper is to construct an analogue of Voevodsky's slice filtration in the motivic unstable homotopy category. The construction is done via birational invariants; this is motivated by the existence of an equivalence of categories between the orthogonal components for Voevodsky's slice filtration and the birational motivic stable homotopy categories constructed by the author in 2013. Another advantage of this approach is that the slices appear naturally as homotopy fibres (and not as in the stable setting, where they are defined as homotopy cofibres) which behave much better in the unstable setting.

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Additional Information

Pablo Pelaez
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8087

Keywords: Birational invariants, motivic homotopy theory, Postnikov tower, slice filtration, unstable slice filtration
Received by editor(s): April 16, 2012
Received by editor(s) in revised form: February 20, 2013
Published electronically: May 22, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.