The Eisenstein ideal at prime-square level has constant rank

• 成果类型: Article
• 署名作者: Lang, Jaclyn; Wake, Preston
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; Michigan State University
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-13793
• DOI: 10.1073/pnas.2500729122
• 发表日期: 2025-07-15
• 关键词: galois representations

摘要

Let N and p be prime numbers with p >= 5 such that p || (N + 1). In a previous paper, we showed that there is a cuspform f of weight 2 and level t0(N2) whose -th pound Fourier coefficient is congruent to pound + 1 modulo a prime above p for all primes pound. In this paper, we prove that this form f is unique up to Galois conjugacy, and the extension of Zp generated by the coefficients of f is exactly Zp[zeta p + 1-1]. We also prove similar results when a higher power of p divides N + 1.