An Abelian Category of Motivic Sheaves

TL;DR

This paper constructs an abelian category of motivic sheaves on algebraic varieties over subfields of C, establishing its properties and connections to classical and Hodge-theoretic sheaves.

Contribution

It introduces a new abelian category of motivic sheaves using Nori's method, linking it to classical sheaves and mixed Hodge structures.

Findings

Category is abelian and has faithful exact realization functors.

Contains a tannakian subcategory of motivic local systems.

All basic geometric examples of variations of mixed Hodge structures arise from this category.

Abstract

The goal of this paper is to construct a category of motivic "sheaves" on an algebraic variety defined over a subfield of C, using Nori's method. This categoryis abelian and it possesses faithful exact realization functors to the categoriesof constructible sheaves for the classical and etale topologies. Moreover, there is a tannakian subcategory of motivic local systems with a realization functor into the category of variations of mixed Hodge structures. Conversely, all basic geometric examples of the latter come from this motivic category.