On a modification of the group of circular units of a real abelian field

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• 作者：Michal Bulant¹ ; ^{bulant@math.muni.cz} ; Radan Ku?era¹ ; ^{kucera@math.muni.cz}
• 关键词：11R20
• 刊名：Journal of Number Theory
• 出版年：2013
• 出版时间：September, 2013
• 年：2013
• 卷：133
• 期：9
• 页码：3138-3148
• 全文大小：225 K

文摘

For a real abelian field K, Sinnott?s group of circular units is a subgroup of finite index in the full group of units playing an important role in Iwasawa theory. Let be the cyclotomic -extension of K, and be the class number of , the n-th layer in . Then for and n going to infinity, the p-parts of the quotients stabilize. Unfortunately this is not the case for , when the group of all units of K, whose squares belong to , is usually used instead of . But is better only for index formula purposes, not having the other nice properties of . The main aim of this paper is to offer another alternative to which can be used in cyclotomic -extensions even for still keeping almost all nice properties of .