Syntomic cohomology as a p-adic absolute Hodge cohomology

The purpose of this paper is to interpret rigid syntomic cohomology defined by Amnon Besser [Bes] as a p-adic absolute Hodge cohomology. This is a p-adic analogue of a work of Beilinson [Be1] which interprets Beilinson-Deligne cohomology in terms of absolute Hodge cohomology. In the process we will define a theory of p-adic absolute Hodge cohomology with coefficients which may be interpreted as a generalization of rigid syntomic cohomology to the case with coefficients.