Washington units, semispecial units, and annihilation of class groups
| Autor: | Radan Kučera, Cornelius Greither |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Class (set theory) Group (mathematics) Generalization Mathematics::Number Theory General Mathematics 010102 general mathematics Field (mathematics) Algebraic geometry 01 natural sciences Number theory 0103 physical sciences Genus field 010307 mathematical physics 0101 mathematics Abelian group Mathematics |
| Zdroj: | manuscripta mathematica. 166:277-286 |
| ISSN: | 1432-1785 0025-2611 |
| DOI: | 10.1007/s00229-020-01241-y |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink