On the Eisenstein ideal over function fields

JOURNAL OF NUMBER THEORY

卷:161

Article

Papikian, Mihran¹  Wei, Fu-Tsun² 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Acad Sinica, Inst Math, Taipei 10617, Taiwan

关键词: Drinfeld modular curves;    Cuspidal divisor group;    Eisenstein ideal;   

DOI  :  10.1016/j.jnt.2015.04.001

来源: Elsevier

【 摘 要 】

We study the Eisenstein ideal of Drinfeld modular curves of small levels, and the relation of the Eisenstein ideal to the cuspidal divisor group and the component groups of Jacobians of Drinfeld modular curves. We prove that the characteristic of the function field is an Eisenstein prime number when the level is an arbitrary non-square-free ideal of F-q [T] not equal to a square of a prime. (C) 2015 Elsevier Inc. All rights reserved.

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