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

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BULANT Michal KUČERA Radan

Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Number Theory
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Doi http://dx.doi.org/10.1016/j.jnt.2013.03.009
Obor Obecná matematika
Klíčová slova Real abelian field; Zp-extension; Group of circular units
Přiložené soubory
Popis 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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