A modular interpretation of BBGS towers

JOURNAL OF NUMBER THEORY

卷:221

Article

Chen, Rui¹  Chen, Zhuo²  Hu, Chuangqiang¹ 

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing, Peoples R China

关键词: Drinfeld module;    Drinfeld modular curve;    Ihara's quantity;    BBGS tower;   

DOI  :  10.1016/j.jnt.2020.06.006

来源: Elsevier

【 摘 要 】

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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free