Syntomic regulators

In this work we introduce different p-adic cohomology theories with a particular ispiration to the Deligne-Beilinson one in the trascendental situation. We will introduce the concept of regulator map as an "higher cycle map" from the higher Chow groups to cohomology theories that we choose to deal with. Our goal is to develop a p-adic theory introduced by Gros and provide a regulator map for it. Some aspect are still open, but this theory allows us to have a connection between Besser and p-adic étale cohomolgy theories in terms of these regulator maps.