### Towards regulator formulae for curves over number fields, by Rob de Jeu

In this paper we study the group K_{2n}^{(n+1)}(F) where F
is the function field of a complete, smooth, geometrically
irreducible curve C over a number field, assuming the
Beilinson--Soul\'e conjecture on weights. In particular, we
compute the Beilinson regulator on a subgroup of K_{2n}^{(n+1)}(F),
using the complexes constructed in previous work by the author.
We study the boundary map in the localization sequence for n = 3
(the case n = 2 was done in a previous paper). We combine our
results with some results of Goncharov in order to obtain a complete
description of the image of the regulator map on K_4^{(3)}(C)
and K_6^{(4)}(C), independent of any conjectures.

Rob de Jeu <jeu@cco.caltech.edu>