Certification of modular Galois representations

Mascot, Nicolas

doi:10.1090/mcom/3215

Certification of modular Galois representations
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by Nicolas Mascot PDF

Math. Comp. 87 (2018), 381-423 Request permission

Abstract:

We show how the output of the algorithm to compute modular Galois representations previously described by the author [Rend. Circ. Mat. Palermo (2) 62 (2013), no. 3, 451–476] 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 nonrational (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 $26$.

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