On the Eisenstein ideal over function fields

2014/10/30 by Mihran Papikian, Papikian, Mihran, Fu-Tsun Wei +2
Mathematics · #11F12 #11G09 #11G18 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F12 #msc:11G09 #msc:11G18

paper · pdf · doi:10.48550/arxiv.1410.8277

42 pages. To appear in J. Number Theory, Special issue in honor of Winnie Li

openalex publication_date 2014/10/30 · arxiv created 2015/05/26 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \mathbbF_q[T] not equal to a square of a prime.

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