A lower bound for the canonical height associated to a Drinfeld module
Abstract
Denis associated to each Drinfeld module M over a global function function field L a canonical height function, which plays a role analogous to that of the Neron-Tate height in the context of elliptic curves. We prove that there exist constants \epsilon>0 and C, depending only on the number of places at which M has bad reduction, such that either x in M is a torsion point of bounded order, or else the canonical height of x is bound below by \epsilon max{h(j_M), deg(D_M)}, where j_M is a certain invariant of the isomorphism class of M, and D_M is the minimal discriminant of M. As an application, we make some observations about specializations of one-parameter families of Drinfeld modules.
Keywords
Cite
@article{arxiv.1210.2340,
title = {A lower bound for the canonical height associated to a Drinfeld module},
author = {Patrick Ingram},
journal= {arXiv preprint arXiv:1210.2340},
year = {2013}
}
Comments
The lower bound in the main result has been significantly improved, and is now essentially sharp for Drinfeld modules with potentially good reduction at all but a bounded number of places