BULANT, Michal and Radan KUČERA. On a modification of the group of circular units of a real abelian field. Journal of Number Theory, Elsevier, 2013, vol. 133, No 9, p. 3138 - 3148. ISSN 0022-314X. doi:10.1016/j.jnt.2013.03.009.
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Basic information
Original name On a modification of the group of circular units of a real abelian field
Authors BULANT, Michal (203 Czech Republic, guarantor, belonging to the institution) and Radan KUČERA (203 Czech Republic, belonging to the institution).
Edition Journal of Number Theory, Elsevier, 2013, 0022-314X.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
Impact factor Impact factor: 0.524
RIV identification code RIV/00216224:14310/13:00066123
Organization unit Faculty of Science
Doi http://dx.doi.org/10.1016/j.jnt.2013.03.009
UT WoS 000320291400021
Keywords in English Real abelian field; Zp-extension; Group of circular units
Tags AKR, rivok
Tags International impact, Reviewed
Changed by Changed by: Ing. Andrea Mikešková, učo 137293. Changed: 8/4/2014 14:18.
Abstract
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.
Links
GAP201/11/0276, research and development projectName: Grupy tříd ideálů algebraických číselných těles
Investor: Czech Science Foundation, Standard Projects
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StarkUnits.pdf   File version Bulant, M. 17/5/2013

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