On a modification of the group of circular units of a real abelian field (Q740860)

Let \(K\) be a real abelian field. The groups \(C_K\) of circular units of Sinnott behave nicely in the ladder of the fields of a \(\mathbb Z_p\)-extension of \(K\), when \(p\) is an odd prime but not as well when \(p=2\). This prompted Sinnott to introduce another group of cyclotomic units to recover this nice behavior for all primes \(p\), though some nice properties of \(C_K\) are lost in the process. The authors exhibit another group of cyclotomic units which replace \(C_K\), with the same features as of those of \(C_K\) and which can be used in \(\mathbb Z_p\)-extensions of \(K\) for all primes \(p\) including \(p=2\). They also compare the behaviour of their groups of cyclotomic units with the behaviour of the usual groups in the layers of a \(\mathbb Z_p\)-extension of \(\mathbb Q\). The paper is well written and proves very interesting for those involved with cyclotomic units.