On a Normal Integral Basis Problem over Cyclotomic Zp-extensions, II

✍ Scribed by Humio Ichimura

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 283 KB
• Volume: 96
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2002.2791

✦ Synopsis

Let p be an odd prime number, K an imaginary abelian field with z p 2 K Â ; and K 1 =K the cyclotomic Z p -extension with its nth layer K n : In the previous paper, we showed that for any n and any unramified cyclic extension L=K n of degree p; LK nþ1 =K nþ1 does have a normal integral basis (NIB) even if L=K n has no NIB, under the assumption that p does not divide the class number of the maximal real subfield K þ (and some additional assumptions on K). In this paper, we show that similar but more delicate phenomena occur for a certain class of tamely ramified extensions of degree p: # 2002 Elsevier Science (USA)