Washington units, semispecial units, and annihilation of class
groups

J 2021

Washington units, semispecial units, and annihilation of class groups

GREITHER, Cornelius Johannes a Radan KUČERA

Základní údaje

Originální název

Washington units, semispecial units, and annihilation of class groups

Autoři

GREITHER, Cornelius Johannes a Radan KUČERA

Vydání

Manuscripta mathematica, Heidelberg, Springer Heidelberg, 2021, 0025-2611

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.640

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/21:00118766

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Washington units; circular (cyclotomic) units; special units; semispecial units.

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 17. 8. 2021 09:25, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA18-11473S, projekt VaV

Název: Grupy tříd ideálů abelovských rozšíření některých číselných těles

Investor: Grantová agentura ČR, Grupy tříd ideálů abelovských rozšíření některých číselných těles

Citovat

GREITHER, Cornelius Johannes a Radan KUČERA. Washington units, semispecial units, and annihilation of class groups. Manuscripta mathematica. Heidelberg: Springer Heidelberg, 2021, roč. 166, 1-2, s. 277-286. ISSN 0025-2611. Dostupné z: https://doi.org/10.1007/s00229-020-01241-y.

@article{1682263,
   author = {Greither, Cornelius Johannes and Kučera, Radan},
   article_location = {Heidelberg},
   article_number = {1-2},
   doi = {https://doi.org/10.1007/s00229-020-01241-y},
   keywords = {Washington units; circular (cyclotomic) units; special units; semispecial units.},
   language = {eng},
   issn = {0025-2611},
   journal = {Manuscripta mathematica},
   title = {Washington units, semispecial units, and annihilation of class groups},
   url = {https://link.springer.com/article/10.1007/s00229-020-01241-y},
   volume = {166},
   year = {2021}
}

TY  - JOUR
ID  - 1682263
AU  - Greither, Cornelius Johannes - Kučera, Radan
PY  - 2021
TI  - Washington units, semispecial units, and annihilation of class groups
JF  - Manuscripta mathematica
VL  - 166
IS  - 1-2
SP  - 277-286
EP  - 277-286
PB  - Springer Heidelberg
SN  - 00252611
KW  - Washington units
KW  - circular (cyclotomic) units
KW  - special units
KW  - semispecial units.
UR  - https://link.springer.com/article/10.1007/s00229-020-01241-y
L2  - https://link.springer.com/article/10.1007/s00229-020-01241-y
N2  - 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.
ER  -

GREITHER, Cornelius Johannes a Radan KUČERA. Washington units, semispecial units, and annihilation of class groups. \textit{Manuscripta mathematica}. Heidelberg: Springer Heidelberg, 2021, roč.~166, 1-2, s.~277-286. ISSN~0025-2611. Dostupné z: https://doi.org/10.1007/s00229-020-01241-y.

Přehled o publikaci