on the eisenstein ideal over function fields

• DOI: 10.48550/arxiv.1410.8277
• Publication Date: 2016-04-01
• Authors: Mihran Papikian; Fu-Tsun Wei
• Keywords: 11G09, 11G18, 11F12; Mathematics - Number Theory; FOS: Mathematics; Number Theory (math.NT); 0101 mathematics; 01 natural sciences

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 $\mathbb{F}_q[T]$ not equal to a square of a prime.<br/>42 pages. To appear in J. Number Theory, Special issue in honor of Winnie Li<br/>