当前位置: X-MOL 学术J. Number Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A modular interpretation of BBGS towers
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.jnt.2020.06.006
Rui Chen , Zhuo Chen , Chuangqiang Hu

In 2000, based on his procedure for constructing explicit towers of modular curves, Elkies deduced explicit equations of rank-2 Drinfeld modular curves which coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth. In 2015, Bassa, Beelen, Garcia, and Stichtenoth constructed a celebrated (recursive and good) tower (BBGS-tower for short) of curves and outlined a modular interpretation of the defining equations. Soon after that, Gekeler studied in depth the modular curves coming from sparse Drinfeld modules. In this paper, to establish a link between these existing results, we propose and prove a generalized Elkies' Theorem which tells in detail how to directly describe a modular interpretation of the equations of rank-m Drinfeld modular curves with m>=2.

中文翻译:

BBGS 塔的模块化诠释

2000 年,根据他构造显式模曲线塔的程序,埃尔基斯推导出了 2 阶 Drinfeld 模曲线的显式方程,该方程与 Garcia 和 Stichtenoth 构造的渐近最优曲线塔重合。2015 年,Bassa、Beelen、Garcia 和 Stichtenoth 构建了一个著名的(递归和良好的)曲线塔(简称 BBGS 塔),并概述了定义方程的模块化解释。不久之后,Gekeler 深入研究了来自稀疏 Drinfeld 模块的模块曲线。在本文中,为了在这些现有结果之间建立联系,我们提出并证明了一个广义 Elkies 定理,该定理详细说明了如何直接描述 m>=2 的秩为 m 的 Drinfeld 模曲线方程的模解释。
更新日期:2021-04-01
down
wechat
bug