On the Gross-Stark Conjecture

• 成果类型: Article
• 署名作者: Dasgupta, Samit; Kakde, Mahesh; Ventullo, Kevin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.188.3.3
• 发表日期: 2018
• 页码: 833-870
• 关键词: totally-real fields; adic l-functions; hilbert modular-forms; EXTENSIONS; cocycles; VALUES

摘要

In 1980, Gross conjectured a formula for the expected leading term at s = 0 of the Deligne-Ribet p-adic L-function associated to a totally even character psi of a totally real field F. The conjecture states that after scaling by L(psi omega(-1), 0), this value is equal to a p-adic regulator of units in the abelian extension of F cut out by psi omega(-1). In this paper, we prove Gross's conjecture.