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

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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Perucca, A., Sgobba, P., & Tronto, S. (2022). Kummer theory for number fields via entanglement groups. Manuscripta Mathematica, 169(1-2), 251-270. https://doi.org/10.1007/s00229-021-01328-0

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Kummer theory for number fields via entanglement groups

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