  In this paper, we give explicit descriptions of Hyodo and Kato's Frobenius
and Monodromy operators on the first $p$-adic de Rham cohomology groups of
curves and Abelian varieties with semi-stable reduction over local fields of
mixed characteristic. This paper was motivated by the first author's paper "A
$p$-adic Shimura isomorphism and periods of modular forms," where conjectural
definitions of these operators for curves with semi-stable reduction were
given.
