Image of I⟩-adic Galois representations modulo p

• 成果类型: Article
• 署名作者: Hida, Haruzo
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0439-7
• 发表日期: 2013
• 页码: 1-40
• 关键词: adic l-functions; hecke algebras; mu-invariant; CONGRUENCE; VALUES; towers

摘要

Let pa parts per thousand yen5 be a prime. If an irreducible component of the spectrum of the 'big' ordinary Hecke algebra does not have complex multiplication, under mild assumptions, we prove that the image of its mod p Galois representation contains an open subgroup of for the canonical weight variable T. This fact appears to be deep, as it is almost equivalent to the vanishing of the mu-invariant of the Kubota-Leopoldt p-adic L-function and the anticyclotomic Katz p-adic L-function. Another key ingredient of the proof is the anticyclotomic main conjecture proven by Rubin/Mazur-Tilouine.