๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Iwasawa Invariants of Real Abelian Number Fields

โœ Scribed by Shu-Leung Tang

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
351 KB
Volume
56
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let k be a real abelian number field and p an odd prime. We give a criterion for the vanishing of the *-invariant for the Z p -extension of k and apply it to give some examples of *=0.

๐Ÿ“œ SIMILAR VOLUMES

Class Numbers and Iwasawa Invariants of
Class Numbers and Iwasawa Invariants of Certain Totally Real Number Fields
โœ Dongho Byeon ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 119 KB

Let p be an odd regular prime number. We prove that there exist infinitely many totally real number fields k of degree p&1 whose class numbers are not divisible by p. Moreover, for certain regular prime number p, we prove that there exist infinitely many totally real number fields k of degree p&1 wh

On a Quotient of the Unramified Iwasawa
On a Quotient of the Unramified Iwasawa Module over an Abelian Number Field
โœ Humio Ichimura ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 154 KB

Let p be a fixed odd prime number and k an imaginary abelian field containing a primitive p th root `p of unity. Let k ร‚k be the cyclotomic Z p -extension and Lร‚k the maximal unramified pro-p abelian extension. We put where E is the group of units of k . Let X=Gal(Lร‚k ) and Y=Gal(L & Nร‚k ), and let

Onp-adicL-functions and Zp-extensions of
Onp-adicL-functions and Zp-extensions of Certain Real Abelian Number Fields
โœ Hisao Taya ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 156 KB

Let k be a real abelian number field with Galois group 2 and p an odd prime number. Denote by k the cyclotomic Z p -extension of k with Galois group 1 and by k n the nth layer of k ร‚k. Assume that the order of 2 is prime to p and that p splits completely in kร‚Q. In this article, we describe the orde

On Number Fields with an Unramified Abel
On Number Fields with an Unramified Abelian Extension of Degree 2n+2
โœ Y.Z. Lan ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 315 KB

Assume that \(K\) is either a totally real or a totally imaginary number field. Let \(F\) be the maximal unramified elementary abelian 2-extension of \(K\) and \([F: K]=2^{n}\). The purpose of this paper is to describe a family of cubic cyclic extension of \(K\). We have constructed an unramified ab