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

DOI10.1007/s10208-021-09505-zOpenAlexW4206708488MaRDI QIDQ2697395

Nicolas Mascot

Publication date: 12 April 2023

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.05885

zbMATH Keywords

algorithmsurfaceunitary groupGalois representationétale cohomologyautomorphic formdévissage\(\mathrm{GL}_3\)

Mathematics Subject Classification ID

Computational aspects of algebraic surfaces (14Q10) Jacobians, Prym varieties (14H40) Other groups and their modular and automorphic forms (several variables) (11F55) Étale and other Grothendieck topologies and (co)homologies (14F20) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) Algebraic number theory computations (11Y40) Computational aspects of algebraic curves (14Q05) Galois representations (11F80) Values of arithmetic functions; tables (11Y70)

Related Items (1)

Hensel-lifting torsion points on Jacobians and Galois representations

Uses Software

• Magma
• PARI/GP
• LMFDB
• GitHub
• LiftTors

Cites Work

• Unnamed Item
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• A non-selfdual automorphic representation of \(\text{GL}_3\) and a Galois representation
• The Magma algebra system. I: The user language
• Companion forms and explicit computation of \(\mathrm{PGL}_2\) number fields with very little ramification
• Computation of étale cohomology on curves in single exponential time
• Computational Aspects of Modular Forms and Galois Representations
• Néron Models
• Gersten's conjecture and the homology of schemes
• Certification of modular Galois representations
• Hensel-lifting torsion points on Jacobians and Galois representations
• Computing Néron–Severi groups and cycle class groups

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