Rubin's conjecture on local units in the anticyclotomic tower at inert primes

• 成果类型: Article
• 署名作者: Burungale, Ashay A.; Kobayashi, Shinichi; Ota, Kazuto
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.194.3.8
• 发表日期: 2021
• 页码: 943-966
• 关键词: elliptic-curves; iwasawa theory; supersingular reduction; main conjectures; points; MODULI; birch

摘要

We prove a fundamental conjecture of Rubin on the structure of local units in the anticyclotomic Z(p)-extension of the unramified quadratic extension of Q(p) for p >= 5 a prime. Rubin's conjecture underlies Iwasawa theory of the anticyclotomic deformation of a CM elliptic curve over the CM field at primes p of good supersingular reduction, notably the Iwasawa main conjecture in terms of the p-adic L -function. As a consequence, we prove an inequality in the p-adic Birch and Swinnerton-Dyer conjecture for Rubin's p-adic L -function. Rubin's conjecture is also an essential tool in our exploration of the arithmetic of Rubin's p-adic L -function, which includes a Bertolini-Darmon-Prasanna type formula.