  If $X$ is a smooth projective variety over ${\mathbb R}$, the Hodge
${\mathcal D}$-conjecture of Beilinson asserts the surjectivity of the
regulator map to Deligne cohomology with real coefficients. It is known to be
false in general but is true in some special cases like Abelian surfaces and
$K3$-surfaces - and still expected to be true when the variety is defined over
a number field. We prove an analogue of this for Abelian surfaces at a
non-Archimedean place where the surface has bad reduction. Here the Deligne
cohomology is replaced by a certain Chow group of the special fibre. The case
of good reduction is harder and was first studied by Spiess in the case of
products of elliptic curve and by me in general.
