  We define an analogue of the `Real' Deligne cohomology group at a prime of
semi-stable or good reduction of a variety. We also define regulator maps to
this group and formulate a conjecture about the image. This allows us to
formulate a non-Archimedian version of Beilinson's Hodge-D-conjecture,
S-integral and function field versions of Beilinson's global conjectures as
well as a precise special value conjecture in the function field case. Finally
we give a few examples where these conjectures are known to be true.
