Construction of with prescribed Iwasawa λ-invariants

✍ Scribed by Satoshi Fujii; Yoshihiro Ohgi; Manabu Ozaki

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 123 KB
• Volume: 118
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2005.09.004

✦ Synopsis

It is a basic problem in Iwasawa theory that the existence of a Z p -extension with prescribed Iwasawa invariants. Since the Iwasawa λ-invariant is regarded as an analogue of (twice of) the genus of an algebraic curve, we are especially interested in the problem on the Iwasawa λ-invariants. In this article, for a few prime numbers p, we show that there is a Z p -extension with prescribed Iwasawa λ-invariant by using Kida's formula, which is a number field analogue of the Riemann-Hurwitz formula.