Bryan Advocaat
Research Subjects
Bryan Advocaat has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Antigona Pajaziti
Les Publications mathématiques de Besançon sont membres du Centre Mersenne pour l'édition scientifique ouverte travail s'appuie sur des résultats en théorie de Kummer Notre
1 shared publication - Antonella Perucca
Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg
1 shared publication - Chi Wa Chan
University of Luxembourg, Esch-Sur-Alzette, Luxembourg
1 shared publication - Flavio Perissinotto
Les Publications mathématiques de Besançon sont membres du Centre Mersenne pour l'édition scientifique ouverte travail s'appuie sur des résultats en théorie de Kummer Notre
1 shared publication
Latest Publications
- Open Access
- 28 August 2025
- Published by MathDoc/Centre Mersenne in Publications mathématiques de Besançon. Algèbre et théorie des nombres
- p. 47-57
Galois groups of Kummer extensions of number fields
Let K be a number field, and let G be a finitely generated subgroup of K × . For every prime number ℓ and for all positive integers m , n with m ⩾ n we show that the structure of the Galois group of the Kummer extension K ( ζ ℓ m , G ℓ n ) / K ( ζ ℓ m ) only depends on G through parameters that express divisibility properties over K (respectively, over K ( ζ 4 ) if ℓ = 2 , ζ 4 ∉ K , m ≥ 2 ). Moreover, we describe an explicit finite procedure to compute at once the Galois group structure for all extensions K ( ζ M , G N ) / K ( ζ M ) with M , N positive integers such that N ∣ M . Our work builds on results in Kummer theory by the last-named author joint with Debry, Hörmann, Perissinotto, Sgobba, and Tronto.
- 28 August 2025
- Published by MathDoc/Centre Mersenne in Publications mathématiques de Besançon. Algèbre et théorie des nombres
- p. 47-57
Open AccessGalois groups of Kummer extensions of number fields
Let K be a number field, and let G be a finitely generated subgroup of K × . For every prime number ℓ and for all positive integers m , n with m ⩾ n we show that the structure of the Galois group of the Kummer extension K ( ζ ℓ m , G ℓ n ) / K ( ζ ℓ m ) only depends on G through parameters that express divisibility properties over K (respectively, over K ( ζ 4 ) if ℓ = 2 , ζ 4 ∉ K , m ≥ 2 ). Moreover, we describe an explicit finite procedure to compute at once the Galois group structure for all extensions K ( ζ M , G N ) / K ( ζ M ) with M , N positive integers such that N ∣ M . Our work builds on results in Kummer theory by the last-named author joint with Debry, Hörmann, Perissinotto, Sgobba, and Tronto.