Norm relations and computational problems in number fields
PAGE, Aurel
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut National de Recherche en Informatique et en Automatique [Inria]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut National de Recherche en Informatique et en Automatique [Inria]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Article de revue
This item was published in
Journal of the London Mathematical Society. 2022-06, vol. 105, n° 4, p. 2373-2414
London Mathematical Society ; Wiley
English Abstract
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 ...Read more >
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.Read less <
ANR Project
Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008
Origin
Hal imported