The De Rham, complex Hodge and p-adic Hodge realization functors on the derived category of relative motives over a field of characteristic zero

2022/03/21 by Johann Bouali, Bouali, Johann
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2203.10875

openalex publication_date 2022/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the categories of geometric mixed Hodge modules on algebraic varieties over a subfield k⊂\mathbb C, and for a prime number p, the categories of geometric p-adic mixed Hodge modules on algebraic varieties over a subfield k⊂ K⊂\mathbb C_p of a p-adic field K. We then give an Hodge realization functor on the de derived category of relative motives over k⊂\mathbb C, and for a prime number p a p-adic Hodge realization functor on the derived category of relative motives over k⊂ K⊂\mathbb C_p.

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