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Towards regulator formulae for curves over number fields

Rob de Jeu
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Abstract

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--Soulé 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.

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Rob de Jeu. 1998-11-05. Towards regulator formulae for curves over number fields. https://arxiv.org/abs/math/9811192

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