The main conjecture of Iwasawa theory for totally real fields

• 成果类型: Article
• 署名作者: Kakde, Mahesh
• 署名单位: University of London; King's College London
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0436-x
• 发表日期: 2013
• 页码: 539-626
• 关键词: zeta-functions; EXTENSIONS; invariant; VALUES

摘要

Let p be an odd prime. Let be a compact p-adic Lie group with a quotient isomorphic to acurrency sign (p) . We give an explicit description of K (1) of the Iwasawa algebra of in terms of Iwasawa algebras of Abelian subquotients of . We also prove a result about K (1) of a certain canonical localisation of the Iwasawa algebra of , which occurs in the formulation of the main conjectures of noncommutative Iwasawa theory. These results predict new congruences between special values of Artin L-functions, which we then prove using the q-expansion principle of Deligne-Ribet. As a consequence we prove the noncommutative main conjecture for totally real fields, assuming a suitable version of Iwasawa's conjecture about vanishing of the cyclotomic mu-invariant. In particular, we get an unconditional result for totally real pro-p p-adic Lie extension of Abelian extensions of ae.