2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68423We 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.15 pagesNumber TheoryAlgebraic Geometry11G40, 11R42,14G25, 11M38text