Mixed motives and motivic birational covers
Copyright policy )Mixed motives and motivic birational covers
We introduce a tower of localizing subcategories in Voevodsky's big (closed under infinite coproducts) triangulated category of motives. We show that the tower induces an interesting finite filtration on the motivic cohomology groups of smooth schemes over a perfect field. With rational coefficients, this finite filtration satisfies several of the properties of the still conjectural Bloch-Beilinson-Murre filtration.
18 pages; exposition simplified, removed unnecessary condition in former proposition 6.1.8
Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Mathematics - Algebraic Geometry, Motivic cohomology; motivic homotopy theory, Mathematics - K-Theory and Homology, Stable homotopy theory, spectra, FOS: Mathematics, K-Theory and Homology (math.KT), Nonabelian homotopical algebra, Algebraic cycles, Algebraic Geometry (math.AG)
Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Applications of methods of algebraic \(K\)-theory in algebraic geometry, Mathematics - Algebraic Geometry, Motivic cohomology; motivic homotopy theory, Mathematics - K-Theory and Homology, Stable homotopy theory, spectra, FOS: Mathematics, K-Theory and Homology (math.KT), Nonabelian homotopical algebra, Algebraic cycles, Algebraic Geometry (math.AG)
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