Certification of modular Galois representations

Certification de représentations galoisiennes modulaires

Nicolas Mascot (1, 2)

1 LFANT - Lithe and fast algorithmic number theory
2 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Galois representations; Certification; Effective Galois theory; Group cohomology

Domaines: Théorie des nombres [math.NT]

Nicolas Mascot. Certification of modular Galois representations. Mathematics of Computation, 2018, 87 (309), pp.381-423. ⟨hal-01426832⟩