Intermediate Jacobians and the slice filtration

TL;DR

The paper explores the structure of motives of smooth projective varieties over complex numbers, proposing new definitions inspired by the slice filtration to understand their decomposition.

Contribution

It introduces novel definitions of certain motive components based on the slice filtration, advancing the understanding of Chow-K"unneth decompositions.

Findings

Proposes definitions of $M_2(X)$ and $M_{2n-2}(X)$ motives.

Provides a framework inspired by the slice filtration.

Enhances the understanding of motive decompositions.

Abstract

For every $n$-dimensional smooth projective variety $X$ over ${\bf C}$, the motive $M(X)$ is expected to admit a Chow-K\"unneth decomposition $M_0(X)\oplus\cdots \oplus M_{2n}(X)$. Inspired by the slice filtration of $M(X)$ we propose the definitions of $M_2(X)$ and $M_{2n-2}(X)$.