The notion of the truncated Euler characteristic for Iwasawa modules is a generalization usual to case when cohomology groups are not finite. Let $p$ be an odd prime, $E_1$ and $E_2$ elliptic curves over number field $F$ with semistable reduction at all primes $v|p$ such that $\operatorname{Gal}(\bar{F}/F)$-modules $E_1[p]$ $E_2[p]$ irreducible isomorphic. We compare invariants certain imprimit...

Let p be a prime number. In the late 1950’s, Kenkichi Iwasawa proved that for a number field F and a Zp extension F∞ of F , that the p-primary part of the class groups of the sub-extensions grow in a manner ruled by three invariants: μ, λ, and ν. A paper by Ralph Greenberg in 1976 studied these invariants when F is totally real and F∞ is the cyclotomic Zp extension, and conjectured that μ = λ =...

A classical twisting lemma says that given a finitely generated torsion module $M$ over the Iwasawa algebra $\mathbb{Z}_p[[\Gamma ]]$ with $\Gamma \cong \mathbb{Z}_p, \exists$ continuous character $\theta: \Gamma \rightarrow \mathbb{Z}_p^\times$ such that, $ \Gamma^{n}$-Euler characteristic of twist $M(\theta)$ is finite for every $n$. This has been generalized general compact $p$-adic Lie gro...

Let K be a number field, let A an abelian variety defined over and $$K_\infty /K$$ uniform p-adic Lie extension. We compare several arithmetic invariants of Iwasawa modules ideal class groups on the one side fine Selmer varieties other side. If $$ contains sufficiently many p-power torsion points A, then we can ranks $$\mu -invariants these algebra. In special cases (e.g. multiple $$\mathbb {Z}...

In this paper we study the Iwasawa theory of Zp-extensions of global function fields k over finite fields of characteristic p. When d = 1 we first show that Iwasawa invariants are well defined under the assumption that only finitely many primes are ramified in the extension, then we prove that the Iwasawa μ-invariant can be arbitrarily large for some extension of any given base field k. After g...

1. Iwasawa functions, p-adic measures, and distributions 1 1.1. Some preliminaries 1 1.2. Iwasawa functions and the Iwasawa algebra 3 1.3. Iwasawa functions and interpolation 4 1.4. p-adic distributions and p-adic measures 8 2. The p-adic L-functions of Dirichlet characters 10 2.1. Preliminaries 10 2.2. Iwasawa’s construction 12 3. The p-adic L-functions of modular forms 15 3.1. Preliminaries 1...

(1) Chromium(0)-Catalyzed Tandem Cyclization of α,β-Unsaturated Thioimidates Containing an Enyne Moiety Karibe, Y.; Kusama, H.; Iwasawa, N.* Angew. Chem. Int. Ed. in press. (2) Efficient Control for the Cationic Platinum(II)-Catalyzed Concise Synthesis of Two Types of Fused Carbocycles with Angular Oxygen Functionality Kusama, H.; Watanabe, E.; Ishida, K.; Iwasawa, N.* Chem.–Asian J. 2011, 6, 2...