Towards regulator formulae for curves over number fields
Rob de Jeu
Abstract
In this paper we study the group K2n(n+1)(F) where F is the function field of a complete, smooth, geometrically irreducible curve C over a number field, assuming the Beilinson--Soulé conjecture on weights. In particular, we compute the Beilinson regulator on a subgroup of K2n(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 K4(3)(C) and K6(4)(C), independent of any conjectures.
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