Some applications of weight structures of Bondarko

TL;DR

This paper constructs a functor linking Voevodsky motives to mixed Hodge structures with integral weights and proves a strong integral version of the Deligne conjecture on 1-motives, advancing the understanding of motives and Hodge theory.

Contribution

It introduces a new functor from Voevodsky motives to a derived category of mixed Hodge structures with integral weights, enabling a stronger form of the Deligne conjecture.

Findings

Established a functor connecting motives and Hodge structures.

Proved a strong integral version of the Deligne conjecture on 1-motives.

Enhanced the understanding of weight structures in the context of motives.

Abstract

We construct a functor from the triangulated category of Voevodsky motives to a certain derived category of mixed Hodge structures enriched with integral weight filtration. We use this construction to prove a strong integral version of the Deligne conjecture on 1-motives which was known previously only up to isogeny.