A Lower Bound for the Canonical Height Associated to a Drinfeld Module

作者：Ingram Patrick^*

来源：International Mathematics Research Notices, 2014, 2014(17): 4879-4916.

DOI：10.1093/imrn/rnt104

Denis associated to each Drinfeld module phi over a global function field L a canonical height h) over cap (phi), which plays a role analogous to that of the Neron-Tate height in the context of elliptic curves. We prove that there exists a constant epsilon > 0, depending only on the number of places at which phi has bad reduction, such that either x is an element of phi(L) is a torsion point of bounded order, or else (h) over cap (phi)(x) >= epsilon max{h(j(phi)), deg(D-phi/L)}, where j(phi) and D-phi/L are analogs of the j-invariant and minimal discriminant of an elliptic curve. As an application, we make some observations about specializations of one-parameter families of Drinfeld modules.

• 出版日期2014