Certification de représentations galoisiennes modulaires

MASCOT, Nicolas

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Licence d’utilisation du document

http://creativecommons.org/licenses/by-nc/

MASCOT, Nicolas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Mathematics of Computation. 2018, vol. 87, n° 309, p. 381–423

American Mathematical Society

Résumé en anglais

We show how the output of the algorithm to compute modular Galois representations described in our previous article can be certified. We have used this process to compute certified tables of such Galois representations obtained thanks to an improved version of this algorithm, including representations modulo primes up to 31 and representations attached to a newform with non-rational (but of course algebraic) coefficients, which had never been done before. These computations take place in the Jacobian of modular curves of genus up to 26. The resulting data are available on the author's webpage.< Réduire

Mots clés en anglais

Galois representations

Certification

Effective Galois theory

Group cohomology

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251