Hodge structures through an étale motivic point of view

2022/12/05 by Ivan Rosas Soto, Soto, Ivan Rosas
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2212.02128

openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the category of étale Chow motives as the étale analogue of Grothendieck motives and proved that it embeds in DM_ét(k). This construction provides a characterization of the generalized Hodge conjecture in terms of an étale analogue of it.

Related

• Chow Künneth decomposition for étale motives
• Réalisations de Hodge des motifs de Voevodsky
• Étale motives of geometric origin
• Pink's theory of Hodge structures and the Hodge conjecture over function fields
• Categorical Künneth formulas for cohomological motives