Washington units, semispecial units, and annihilation of class groups

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Washington units, semispecial units, and annihilation of class groups

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Washington units, semispecial units, and annihilation of class groups

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-11473S" target="_blank" >GA18-11473S: Grupy tříd ideálů abelovských rozšíření některých číselných těles</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Manuscripta mathematica

ISSN

0025-2611

e-ISSN

1432-1785

Svazek periodika

166

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

10

Strana od-do

277-286

Kód UT WoS článku

000566859400001

EID výsledku v databázi Scopus

2-s2.0-85090308384