The Bogomolov conjecture is a finiteness statement about algebraic points of small height on a
smooth complete curve defined over a global field. We verify an effective form of the Bogomolov
conjecture for all curves of genus at most $4$ over a function field of characteristic zero.
We recover the known result for genus-$2$ curves and in many cases improve upon the known bound for
genus-$3$ curves. For many curves of genus $4$ with bad reduction, the conjecture was previously unproved.
Publié le : 2009-05-15
Classification:
Bogomolov conjecture,
curves of higher genus,
function fields,
metric graphs,
11G30,
14G40,
11G50
@article{1259158471,
author = {Faber, X. W. C.},
title = {The Geometric Bogomolov Conjecture for Curves of Small Genus},
journal = {Experiment. Math.},
volume = {18},
number = {1},
year = {2009},
pages = { 347-367},
language = {en},
url = {http://dml.mathdoc.fr/item/1259158471}
}
Faber, X. W. C. The Geometric Bogomolov Conjecture for Curves of Small Genus. Experiment. Math., Tome 18 (2009) no. 1, pp. 347-367. http://gdmltest.u-ga.fr/item/1259158471/