Certification of modular Galois representations

DOI10.1090/mcom/3215zbMath1422.11127arXiv1312.6418OpenAlexW2951638131MaRDI QIDQ4586623

Nicolas Mascot

Publication date: 30 October 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6418

Mathematics Subject Classification ID

Galois theory (11S20) Cohomology of groups (20J06) Holomorphic modular forms of integral weight (11F11) Algebraic number theory computations (11Y40) Galois representations (11F80)

Related Items

Companion forms and explicit computation of \(\mathrm{PGL}_2\) number fields with very little ramification, Moduli-friendly Eisenstein series over the \(p\)-adics and the computation of modular Galois representations, Explicit computation of a Galois representation attached to an eigenform over \(\mathrm{SL}_3\) from the \(\mathrm{H}_{\acute{\mathrm{e}}\mathrm{t}}^2\) of a surface, Hensel-lifting torsion points on Jacobians and Galois representations

Uses Software

• Magma
• PARI/GP
• SageMath

Cites Work

• Computing modular Galois representations
• Identifying Frobenius elements in Galois groups
• Serre's modularity conjecture. I
• Liftings of projective 2-dimensional Galois representations and embedding problems
• The Magma algebra system. I: The user language
• Refinement of Tate's discriminant bound and non-existence theorems for mod \(p\) Galois representations
• A tameness criterion for Galois representations associated to modular forms (mod \(p\))
• Computational Aspects of Modular Forms and Galois Representations
• on l-adic representations attached to modular forms II
• The irreducibility of some level 1 Hecke polynomials
• Computation of Galois groups of rational polynomials
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