The anabelian Isom-conjecture of Grothendieck concerns the fact that the isomorphism class of certain types of varieties is uniquely determined by their étale fundamental groups. While in the case of affine curves over a finite field the Isom-conjecture was solved by Tamagawa, up to now almost nothing is known for arithmetic curves. We discuss a new approach to a group-theoretic charachterization of the decomposition subgroups of points inside the étale fundamental group (assuming some still unknown properties of it), which uses the regulators of certain intermediate number fields. This leads us to the more realistic hope to prove a weaker version of the Isom-conjecture, which allows to recover the curve from its Weil-étale fundamental group.