BIASSE, Jean‐françois; FIEKER, Claus; HOFMANN, Tommy; PAGE, Aurel

doi:10.1112/jlms.12563

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BIASSE, Jean‐françois
University of South Florida [Tampa] [USF]

FIEKER, Claus
Technische Universität Kaiserslautern [TU Kaiserslautern]

HOFMANN, Tommy
Technical University of Kaiserslautern [TU Kaiserslautern]

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Ce document a été publié dans

Journal of the London Mathematical Society. 2022-06, vol. 105, n° 4, p. 2373-2414

London Mathematical Society ; Wiley

Résumé en anglais

For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathbb{Q}[G]$. We give necessary and sufficient criteria for the existence of such relations and apply them to obtain relations between the arithmetic invariants of the subfields of an algebraic number field with Galois group $G$. On the algorithm side this leads to subfield based algorithms for computing rings of integers, $S$-unit groups and class groups. For the $S$-unit group computation this yields a polynomial-time reduction to the corresponding problem in subfields. We compute class groups of large number fields under GRH, and new unconditional values of class numbers of cyclotomic fields.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192399

DOI

http://dx.doi.org/10.1112/jlms.12563

Project ANR

Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008

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Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251