TY - JOUR
T1 - Kummer theory for number fields via entanglement groups
AU - Perucca, Antonella
AU - Sgobba, Pietro
AU - Tronto, Sebastiano
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/9
Y1 - 2022/9
N2 - Let K be a number field, and let G be a finitely generated subgroup of K×. We are interested in computing the degree of the cyclotomic-Kummer extension K(Gn) over K, where Gn consists of all n-th roots of the elements of G. We develop the theory of entanglements introduced by Lenstra, and we apply it to compute the above degrees.
AB - Let K be a number field, and let G be a finitely generated subgroup of K×. We are interested in computing the degree of the cyclotomic-Kummer extension K(Gn) over K, where Gn consists of all n-th roots of the elements of G. We develop the theory of entanglements introduced by Lenstra, and we apply it to compute the above degrees.
UR - http://www.scopus.com/inward/record.url?scp=85112817102&partnerID=8YFLogxK
U2 - 10.1007/s00229-021-01328-0
DO - 10.1007/s00229-021-01328-0
M3 - Article
AN - SCOPUS:85112817102
SN - 0025-2611
VL - 169
SP - 251
EP - 270
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 1-2
ER -