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. Received: 25 September 2000 / In final form: 23 March 2001 / Published online: 28 February 2002