The Karoubi regulator and syntomic regulators

A. Besser

Abstract

This is a report on work in progress. We generalize a construction of Karoubi and define a regulator from the algebraic K-theory of a variety X over a p-adic field to a cohomology theory similar in style to Karoubi's ``multiplicative K-theory". In some cases this cohomology should simply be syntomic cohomology up torsion. The advantage is that the regulator depends only on X and not on an integral model. We discuss a possible application to the syntomic regulator of fields.