Voevodsky's slice conjectures via Hilbert schemes

TL;DR

This paper provides new, conceptual proofs of Voevodsky's slice conjectures by leveraging motivic infinite loop space theory and the birational geometry of Hilbert schemes, offering an alternative to Levine's homotopy coniveau tower approach.

Contribution

It introduces a novel, conceptual approach to prove Voevodsky's slice conjectures using motivic homotopy theory and Hilbert schemes, simplifying previous proofs.

Findings

Short and conceptual proofs of Voevodsky's slice conjectures.

Application of motivic infinite loop space theory to algebraic geometry.

Connection between slice filtration and birational geometry of Hilbert schemes.

Abstract

Using recent development in motivic infinite loop space theory, we offer short and conceptual reproofs of some conjectures of Voevodsky's on the slice filtration using the birational geometry of Hilbert schemes. The original proofs were due to Marc Levine using very different methods, namely, the homotopy coniveau tower.