Purely additive reduction of abelian varieties with torsion

DOI10.1016/j.jnt.2021.10.015zbMath1491.11061arXiv2111.15315OpenAlexW3217597740WikidataQ114156664 ScholiaQ114156664MaRDI QIDQ2671991

Mentzelos Melistas

Publication date: 8 June 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.15315

zbMATH Keywords

abelian varietyNéron modeltorsion pointpurely additive reductionKodaira type

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Abelian varieties of dimension (> 1) (11G10) Arithmetic ground fields for abelian varieties (14K15)

Related Items (2)

Torsion and twists of abelian varieties ⋮ On a conjecture of Agashe

Uses Software

• Magma
• Mathematica
• SageMath

Cites Work

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• On Néron's classification of elliptic curves of residue characteristics 2 and 3
• The Néron model over the Igusa curves
• Abelian varieties having purely additive reduction
• A note on elliptic curves with a rational 3-torsion point
• Die stabile Reduktion der Fermatkurve über einem Zahlkörper. (The stable reduction of the Fermat curve over a number field)
• Galois properties of torsion points on abelian varieties
• Some remarks concerning points of finite order on elliptic curves over global fields
• Some results on the Mordell-Weil group of the Jacobian of the Fermat curve
• The Magma algebra system. I: The user language
• Unipotent groups and curves of genus two
• Néron models
• Continued fractions for rational torsion
• Large rational torsion on abelian varieties
• Semistable reduction and torsion subgroups of abelian varieties
• The complete classification of fibres in pencils of curves of genus two
• Special fibers of Néron models and wild ramification
• Computation on elliptic curves with complex multiplication
• Algebraic Groups
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Structure de torsion des courbes elliptiques sur les corps quadratiques
• On the group of components of a Néron model.
• Local Bounds for Torsion Points on Abelian Varieties
• The Arithmetic of Elliptic Curves
• Néron Models
• Modèles minimaux des courbes de genre deux.
• Elliptic Curves
• Jacobians of Genus-2 Curves with a Rational Point of Order 11

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