Chabauty Without the Mordell-Weil Group

DOI10.1007/978-3-319-70566-8_28zbMath1425.11131arXiv1506.04286OpenAlexW1621039055MaRDI QIDQ4556596

Michael Stoll

Publication date: 16 November 2018

Published in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.04286

zbMATH Keywords

rational points on curvesSelmer groupChabauty's method

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Computer solution of Diophantine equations (11Y50) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Higher degree equations; Fermat's equation (11D41) Global ground fields in algebraic geometry (14G25)

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Uses Software

• Magma
• OEIS

Cites Work

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• Most odd degree hyperelliptic curves have only one rational point
• Exhibiting SHA[2 on hyperelliptic Jacobians]
• Finite descent obstructions and rational points on curves
• On the method of Coleman and Chabauty
• The Magma algebra system. I: The user language
• Odd degree number fields with odd class number
• 2-descent on the Jacobians of hyperelliptic curves
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Two-cover descent on hyperelliptic curves
• The Mordell–Weil sieve: proving non-existence of rational points on curves
• How to do a 𝑝-descent on an elliptic curve
• Explicit Coleman Integration for Hyperelliptic Curves
• Independence of rational points on twists of a given curve
• Perfect powers expressible as sums of two fifth or seventh powers
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point