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

Johann Bouali (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We introduce the categories of geometric complex mixed Hodge modules on algebraic varieties over a subfield k ⊂ C, and for a prime number p, the categories of p-adic mixed Hodge modules on algebraic varieties over a subfield k ⊂ Cp. We then give a complex Hodge realization functor on the derived category of relative motives over k ⊂ C and a p-adic Hodge realization functor on the derived category of relative motives over k ⊂ Cp.

Domains: Mathematics [math]

Johann Bouali. The De Rham, complex Hodge and p-adic Hodge realization functor on the derived category of relative motives over a field of characteristic zero. 2022. ⟨hal-03615090v3⟩