R\'ealisation de de Rham des motifs de Voevodsky

TL;DR

This paper reviews motives and details the construction of a de Rham realization functor from geometric mixed motives to bifiltered vector spaces, following Deligne-Goncharov's approach.

Contribution

It provides a detailed construction of the de Rham realization functor for geometric mixed motives, expanding on existing theoretical frameworks.

Findings

Explicit construction of the de Rham realization functor

Clarification of the relationship between motives and bifiltered vector spaces

Extension of Deligne-Goncharov's methodology

Abstract

After reviewing some basic facts about pure and mixed motives, we explain, following Deligne-Goncharov, how to construct a de Rham realisation functor from the category of geometric mixed motives to the category of bifiltered vector spaces.