Work

Computing class groups by induction with generalised norm relations

Year: 2024

Type: preprint

Abstract: We introduce a generalisation of norm relations in the group algebra Q[G], where G is a finite group. We give some properties of these relations, and use them to obtain relations between the S-unit groups of different subfields of the same Galois extension of Q, of Galois group G. Then we deduce an algorithm to compute the class groups of some number fields by reducing the problem to fields of lower degree. We compute the class groups of some large number fields.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.13124

Author: Etienne, Fabrice

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Centre National de la Recherche Scientifique, Université de Bordeaux

Awards: Cryptography, Isogenies and Abelian varieties Overwhelming, G3010527862, Cryptographic hardness of module lattices, Cryptanalyse de primitives cryptographiques classiques

OpenAlex ID: W6948322005

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