On the p-adic beilinson conjecture for number fields

We formulate a conjectural p-adic analogue of Borel's theorem relating regulators for higher K-groups of number fields to special values of the corresponding ζ-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of the conjectures are proved when the number field (or Artin motive) is Abelian over the rationals, and all conjectures are verified numerically in various other cases.