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Voevodsky’s slice conjectures via Hilbert schemes. (English) Zbl 1471.19003

Summary: We offer short and conceptual re-proofs of some conjectures of Voevodsky’s on the slice filtration. The original proofs were due to Marc Levine using the homotopy coniveau tower. Our new proofs use very different methods, namely, recent development in motivic infinite loop space theory together with the birational geometry of Hilbert schemes.

MSC:

19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14F42 Motivic cohomology; motivic homotopy theory
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