Kummer theory for number fields via entanglement groups

Antonella Perucca; Pietro Sgobba; Sebastiano Tronto

doi:10.1007/s00229-021-01328-0

Kummer theory for number fields via entanglement groups

Antonella Perucca^*
, Pietro Sgobba
, Sebastiano Tronto

^*Corresponding author for this work

University of Luxembourg

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	251-270
Number of pages	20
Journal	Manuscripta Mathematica
Volume	169
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-021-01328-0
Publication status	Published - Sept 2022
Externally published	Yes

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10.1007/s00229-021-01328-0

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title = "Kummer theory for number fields via entanglement groups",

abstract = "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.",

author = "Antonella Perucca and Pietro Sgobba and Sebastiano Tronto",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Perucca, Antonella

AU - Sgobba, Pietro

AU - Tronto, Sebastiano

PY - 2022/9

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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 - https://www.scopus.com/pages/publications/85112817102

U2 - 10.1007/s00229-021-01328-0

DO - 10.1007/s00229-021-01328-0

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SP - 251

EP - 270

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 1-2

ER -

Kummer theory for number fields via entanglement groups

Abstract

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