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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00066123" target="_blank" >RIV/00216224:14310/13:00066123 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jnt.2013.03.009" target="_blank" >http://dx.doi.org/10.1016/j.jnt.2013.03.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2013.03.009" target="_blank" >10.1016/j.jnt.2013.03.009</a>

Result language
angličtina
Original language name
On a modification of the group of circular units of a real abelian field
Original language 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 numberof 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F11%2F0276" target="_blank" >GAP201/11/0276: Ideal class groups of algebraic number fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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