The kernel of the Eisenstein ideal

JOURNAL OF NUMBER THEORY

卷:92

Article

Csirik, JA

关键词: modular curves;    Eisenstein ideal;   

DOI  :  10.1006/jnth.2001.2709

来源: Elsevier

【 摘 要 】

Let N be a prime number, and let J(0)(N) be the Jacobian of the modular curve X-0(N). Let T denote the endomorphism ring of J(0)(N). In a seminal 1977 article, B. Mazur introduced and studied an important ideal I subset of or equal to T, the Eisenstein ideal. In this paper we give an explicit construction of the kernel J(0)(N)[I] of this ideal (the set of points in J(0)(N) that are annihilated by all elements of 1). We use this construction to determine the action of the group Gal((Q) over bar /Q) on J(0)(N)[I]. Our results were previously known in the special case where N - 1 is not divisible by 16. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free