Hensel-lifting torsion points on Jacobians and Galois representations

DOI10.1090/mcom/3484zbMath1458.11088arXiv1808.03939OpenAlexW2965297591MaRDI QIDQ5216734

Nicolas Mascot

Publication date: 18 February 2020

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

Full work available at URL: https://arxiv.org/abs/1808.03939

zbMATH Keywords

algorithmJacobianGalois representation\(p\)-adic

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Local ground fields in algebraic geometry (14G20) Algebraic number theory computations (11Y40) Computational aspects of algebraic curves (14Q05) Galois representations (11F80)

Related Items (5)

Moduli-friendly Eisenstein series over the \(p\)-adics and the computation of modular Galois representations ⋮ Geometric quadratic Chabauty and \(p\)-adic heights ⋮ 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 ⋮ LiftTors ⋮ Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture

Uses Software

• GAP
• Magma
• PARI/GP
• LMFDB
• GitHub

Cites Work

• Computing modular Galois representations
• Identifying Frobenius elements in Galois groups
• Efficient computation of addition chains
• The Magma algebra system. I: The user language
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• The Weil pairing, and its efficient calculation
• Improved complexity bounds for counting points on hyperelliptic curves
• 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
• Computing in Picard groups of projective curves over finite fields
• Asymptotically fast group operations on Jacobians of general curves
• Generators for the ℓ-Torsion Subgroup of Jacobians of Genus Two Curves
• The Arithmetic of Elliptic Curves
• Spans in the module (Z_m)^s
• A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
• Linear algebra algorithms for divisors on an algebraic curve
• Certification of modular Galois representations
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results
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