Washington units, semispecial units, and annihilation of class groups
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118766" target="_blank" >RIV/00216224:14310/21:00118766 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00229-020-01241-y" target="_blank" >https://link.springer.com/article/10.1007/s00229-020-01241-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00229-020-01241-y" target="_blank" >10.1007/s00229-020-01241-y</a>
Alternative languages
Result language
angličtina
Original language name
Washington units, semispecial units, and annihilation of class groups
Original language description
Special units are a sort of predecessor of Euler systems, and they are mainly used to obtain annihilators for class groups. So one is interested in finding as many special units as possible (actually we use a technical generalization called “semispecial”). In this paper we show that in any abelian field having a real genus field in the narrow sense all Washington units are semispecial, and that a slightly weaker statement holds true for all abelian fields. The group of Washington units is very often larger than Sinnott’s group of cyclotomic units. In a companion paper we will show that in concrete families of abelian fields the group of Washington units is much larger than that of Sinnott units, by giving lower bounds on the index. Combining this with the present paper gives strong annihilation results.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-11473S" target="_blank" >GA18-11473S: The ideal class groups of abelian extensions of some number fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Manuscripta mathematica
ISSN
0025-2611
e-ISSN
1432-1785
Volume of the periodical
166
Issue of the periodical within the volume
1-2
Country of publishing house
DE - GERMANY
Number of pages
10
Pages from-to
277-286
UT code for WoS article
000566859400001
EID of the result in the Scopus database
2-s2.0-85090308384