Towards a conjecture of Sharifi

JOURNAL OF NUMBER THEORY

卷:222

Article

Wang, Jun¹ 

[1] Univ British Columbia, Dept Math, Vancouver, BC, Canada

关键词: Eisenstein ideal;    Modular symbols;    Sharifi's conjectures;   

DOI  :  10.1016/j.jnt.2020.12.016

来源: Elsevier

【 摘 要 】

We apply the methods of Fukaya, Kato and Sharifi to refine Mazur's study of the Eisenstein ideal. Given prime numbers N and p >= 5 such that p vertical bar phi(N), we study the quotient of the cohomology group of modular curve X-0(N) by the square of the Eisenstein ideal. We study two invariants b, c attached to this quotient and compute c. We propose a conjecture about the invariant b which relates the structure of the ray class group of conductor N to the modular symbols of X-0(N). Assuming this conjecture, we compute the invariant b. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free