Geodesic
On the compositum of orthogonal cyclic fields of the same odd prime degree
Canadian journal of mathematics, Tome 73 (2021) no. 6, pp. 1506-1530

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DOI

The aim of this paper is to study circular units in the compositum K of t cyclic extensions of ${\mathbb {Q}}$ ($t\ge 2$) of the same odd prime degree $\ell $. If these fields are pairwise arithmetically orthogonal and the number s of primes ramifying in $K/{\mathbb {Q}}$ is larger than $t,$ then a nontrivial root $\varepsilon $ of the top generator $\eta $ of the group of circular units of K is constructed. This explicit unit $\varepsilon $ is used to define an enlarged group of circular units of K, to show that $\ell ^{(s-t)\ell ^{t-1}}$ divides the class number of K, and to prove an annihilation statement for the ideal class group of K.
DOI : 10.4153/S0008414X20000589
Mots-clés : Circular (cyclotomic) units, absolutely abelian fields, class groups 
Greither, Cornelius; Kučera, Radan. On the compositum of orthogonal cyclic fields of the same odd prime degree. Canadian journal of mathematics, Tome 73 (2021) no. 6, pp. 1506-1530. doi: 10.4153/S0008414X20000589
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     title = {On the compositum of orthogonal cyclic fields of the same odd prime degree},
     journal = {Canadian journal of mathematics},
     pages = {1506--1530},
     year = {2021},
     volume = {73},
     number = {6},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000589/}
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