R\'ealisations de Hodge des motifs de Voevodsky
Florence Lecomte (IRMA), Nathalie Wach (IRMA)

TL;DR
This paper constructs Hodge realizations of Voevodsky motives over subfields of complex numbers, using mixed Hodge complexes and filtrations, and introduces a Deligne-Beilinson realization, advancing the understanding of motivic cohomology.
Contribution
It provides a new construction of Hodge and Deligne-Beilinson realizations for Voevodsky motives using filtrations and complexes, improving previous frameworks.
Findings
Hodge realization as cohomology of mixed Hodge DG-complex
Representation of filtrations via truncation functors
Construction of Deligne-Beilinson realization
Abstract
Over a subfield of the field of complex numbers, the Hodge realization of a geometrical motive is defined and represented as the cohomology of a mixed Hodge DG-complex in the sense of Deligne. Both filtrations are represented by truncation functors, on a Bondarko weight complex for the weight filtration and on the De Rham motivic complex for the Hodge one. The Deligne-Beilinson realization is also constructed. This preprint partially replaces the former "R\'ealisation des complexes motiviques de Voevodsky".
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