TL;DR
This paper introduces a new filtration on motivic cohomology groups using a tower of localizing subcategories, providing insights related to the conjectural Bloch-Beilinson-Murre filtration.
Contribution
It constructs a novel tower of localizing subcategories in Voevodsky's motives category that induces a finite filtration on motivic cohomology.
Findings
Finite filtration on motivic cohomology groups.
Properties resemble the conjectural Bloch-Beilinson-Murre filtration.
Applicable to smooth schemes over perfect fields.
Abstract
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.
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