On a modification of the group of circular units of a real abelian field
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Number Theory |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.jnt.2013.03.009 |
| Field | General mathematics |
| Keywords | Real abelian field; Zp-extension; Group of circular units |
| Attached files | |
| Description | For a real abelian field K, Sinnott's group of circular units C_K is a subgroup of finite index in the full group of units E_K playing an important role in Iwasawa theory. Let K_infty/K be the cyclotomic Z(p)-extension of K, and h(Kn) be the class number of K_n, the n-th layer in K_infty/K. Then for p<>2 and n going to infinity, the p-parts of the quotients [E_Kn : C_Kn]/h(Kn) stabilize. Unfortunately this is not the case for p=2, when the group C_1K of all units of K, whose squares belong to C_K, is usually used instead of C_K. But C_1K is better only for index formula purposes, not having the other nice properties of C_K. The main aim of this paper is to offer another alternative to C_K which can be used in cyclotomic Z(p)-extensions even for p=2 still keeping almost all nice properties of C_K. |
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