Slices and Transfers
Slices and Transfers
We study the slice filtration for S^1-spectra over a field k, and raise a number of questions regardings its properties. We show that the slices, except for the 0th slice, admit a further filtration whose layers are in a natural way the Eilenberg-Maclane spectra associated to a homotopy invariant complex of Nisnevic sheaves with transfer, i.e., an effective motive. We give an example to show that in general the 0th slice does not admit transfers.
39 pages
- Northwestern University United States
Morel-Voevodsky stable homotopy category, 14C25, 19E15, Stable homotopy theory, spectra, K-Theory and Homology (math.KT), Algebraic cycles, algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Mathematics - Algebraic Geometry, Motivic cohomology; motivic homotopy theory, Mathematik, Mathematics - K-Theory and Homology, FOS: Mathematics, slice filtration, Algebraic Geometry (math.AG), \(K\)-theory of schemes
Morel-Voevodsky stable homotopy category, 14C25, 19E15, Stable homotopy theory, spectra, K-Theory and Homology (math.KT), Algebraic cycles, algebraic cycles, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Mathematics - Algebraic Geometry, Motivic cohomology; motivic homotopy theory, Mathematik, Mathematics - K-Theory and Homology, FOS: Mathematics, slice filtration, Algebraic Geometry (math.AG), \(K\)-theory of schemes
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