On K_2 of certain families of curves
K-Theory and Homology
2014-09-22 v2 Number Theory
Abstract
We construct families of smooth, proper, algebraic curves in characteristic 0, of arbitrary genus g, together with g elements in the kernel of the tame symbol. We show that those elements are in general independent by a limit calculation of the regulator. Working over a number field, we show that in some of those families the elements are integral. We determine when those curves are hyperelliptic, finding, in particular, that over any number field we have non-hyperelliptic curves of all composite genera g with g independent integral elements in the kernel of the tame symbol.
Cite
@article{arxiv.1402.4822,
title = {On K_2 of certain families of curves},
author = {Hang Liu and Rob de Jeu},
journal= {arXiv preprint arXiv:1402.4822},
year = {2014}
}
Comments
Revised version: improved exposition. some sections split