منابع مشابه
Multiplicative Properties of the Slice Filtration
Introduction Let S be a Noetherian separated scheme of finite dimension, and let SH(S) denote the motivic stable homotopy category of Morel and Voevodsky. In order to get a motivic version of the Postnikov tower, Voevodsky [23] constructs a filtered family of triangulated subcategories of SH(S):
متن کاملThe slice filtration and mixed Tate motives
Using the ”slice filtration”, defined by effectivity conditions on Voevodsky’s triangulated motives, we define spectral sequences converging to their motivic cohomology and étale motivic cohomology. These spectral sequences are particularly interesting in the case of mixed Tate motives as their E2-terms then have a simple description. In particular this yields spectral sequences converging to t...
متن کاملThe Equivariant Slice Filtration: a Primer
We present an introduction to the equivariant slice filtration. After reviewing the definitions and basic properties, we determine the sliceconnectivity of various families of naturally arising spectra. This leads to an analysis of pullbacks of slices defined on quotient groups, producing new collections of slices. Building on this, we determine the slice tower for the Eilenberg-Mac Lane spectr...
متن کاملBirational 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), Thom spaces and blow ups. 2000 Mathematics Subject Classification: 14F42
متن کاملSlice filtration on motives and the Hodge conjecture
The slice filtration on Voevodsky’s triangulated category of motives is defined by effectivity conditions. It is constructed and studied in [HK]. An analogous filtration on the homotopy category was introduced by Voevodsky. In this note we try to get a conjectural picture of the properties of the slice filtration by systematic use of the realization functor to the derived category of Hodge stru...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06116-3