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

Abstract

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

arXiv admin note: substantial text overlap with arXiv:2007.02446

Cited by in corpus (2)

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