Publication details

Washington units, semispecial units, and annihilation of class groups


GREITHER Cornelius Johannes KUČERA Radan

Year of publication 2021
Type Article in Periodical
Magazine / Source Manuscripta mathematica
MU Faculty or unit

Faculty of Science

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