Towards regulator formulae for curves over number fields
Number Theory
2007-05-23 v1 Algebraic Geometry
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--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.
Cite
@article{arxiv.math/9811192,
title = {Towards regulator formulae for curves over number fields},
author = {Rob de Jeu},
journal= {arXiv preprint arXiv:math/9811192},
year = {2007}
}