Nori motives (and mixed Hodge modules) with integral coefficients

TL;DR

This paper constructs integral Nori motivic sheaves and mixed Hodge modules with six operations and descent properties, advancing the understanding of motives with integral coefficients.

Contribution

It introduces abelian categories of integral Nori motives and develops their six operations and descent theory, including for mixed Hodge modules over the reals.

Findings

Constructed abelian categories of integral Nori motives.

Developed a t-structure on modules over an algebra in étale motives.

Established six operations and arc-descent for these categories.

Abstract

We construct abelian categories of integral Nori motivic sheaves over a scheme of characteristic zero. The first step is to study the presentable derived category of Nori motives over a field. Next we construct an algebra in \'etale motives such that modules over it afford a t-structure that restricts to constructible objects. This category of integral Nori motives has the six operations and arc-descent. We finish by providing analogous constructions and results for mixed Hodge modules on schemes over the reals.