The Euler system of cyclotomic units and higher Fitting ideals

2009/12/24 by Tatsuya Ohshita, Ohshita, Tatsuya
Mathematics · #11R18 #11R23 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0912.4854

openalex publication_date 2009/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Kurihara established a refinement of the minus-part of the Iwasawa main conjecture for totally real number fields using the higher Fitting ideals. In this paper, we study the higher Fitting ideals of the plus-part of the Iwasawa module associated to the cyclotomic Z_p-extension of Q(μ_p) for an odd prime number p by similar methods as in Kurihara's work. We define the higher cyclotomic ideals C_i, which are ideals of the Iwasawa algebra defined by the Kolyvagin derivatives of cyclotomic units, and prove that they give upper bounds of the higher Fitting ideals. Our result can be regarded as a refinement of the plus-part of the Iwasawa main conjecture for Q.

Related

• On the higher Fitting ideals of Iwasawa modules of ideal class groups over real abelian fields
• On higher Fitting ideals of Iwasawa modules of ideal class groups over imaginary quadratic fields and Euler systems of elliptic units II
• On units generated by Euler systems
• A higher rank Euler system for the multiplicative group over a totally real field
• On Weil Numbers in Cyclotomic Fields