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arXiv · 1210.2340

A lower bound for the canonical height associated to a Drinfeld module

Patrick Ingram
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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 ε>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 εmax{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.

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Patrick Ingram. 2012-12-29. A lower bound for the canonical height associated to a Drinfeld module. https://arxiv.org/abs/1210.2340

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