  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 $k\subset
K\subset\mathbb C_p$.
