The Local Lehmer Inequality For Drinfeld Modules

Lehmer problem and Drinfeld modules

We propose a lower bound estimate in Dobrowolski's style of the canonical height on a certain family of Drinfeld modules of characteristic 0, including under some hypothesis on their degree and their base field, the complex multiplication case, extending so a previous result of L. Denis on Carlitz modules. Our study is focused on the highest possible level of precision on the parameters involved with rapport to the main values which characterize the Drinfeld module (height, base field degree and rank) and it provides an estimate in function of both separable and inseparable degree of the algeb…

Lehmer Inequality and the Mordell-Weil Theorem for Drinfeld modules

In this paper we prove a special case of the Lehmer inequality for Drinfeld modules. Also, based on this inequality, we prove certain Mordell-Weil type of theorems for certain infinitely generated fields.

Drinfeld模的平行四边形高度不等式

A parallelogram height inequality for Drinfeld modules

本文研究了Drinfeld模在平行四边形同态结构下的高度不等式，类比于数域和函数域上阿贝尔簇的相关结果。

Drinfeld模的局部单值性

Local monodromy of Drinfeld modules

针对Drinfeld模局部单值性复杂的问题，提出局部导子不变量，用局部周期格体积给出其上界，发展函数域赋范格理论并联系向量丛正则性，还描述大剩余秩Drinfeld模的惯性像性质。

A combinatorial Li-Yau inequality and rational points on curves

We present a method to control gonality of nonarchimedean curves based on graph theory. Let k denote a complete nonarchimedean valued field. We first prove a lower bound for the gonality of a curve over the algebraic closure of k in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-called finite harmonic graph morphisms to trees, that originate from any refinement of the dual graph of the stable model of the curve. Next comes our main result: we prove a lower bound for the degree of such a graph morphism in terms of the first eigenvalue of the Laplac…