Lower Bounds for the Canonical Height on Drinfeld Modules

被引：3

作者：

Bosser, Vincent ^{[1
]}

Galateau, Aurelien ^{[2
]}

机构：

[1] Univ Caen, Caen, France

[2] Univ Franche Comte, Besancon, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2019年 / 2019卷 / 01期

关键词：

MORDELL-WEIL THEOREM; NERON-TATE HEIGHT; LEHMER INEQUALITY;

D O I：

10.1093/imrn/rnx112

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use diophantine approximation to bound from below the canonical height on a Drinfeld module. We first give a positive answer to the Lehmer problem in the case of purely inseparable extensions on Drinfeld modules with at least one supersingular prime. We also revisit the CM case, where we improve the estimates already known, and we finally give a bound of polynomial strength in the general case.

引用

页码：165 / 200

页数：36

共 28 条

[1] A lower bound for the height in Abelian extensions [J].