A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves

DOI10.1007/s00208-018-1684-xzbMath1460.11038arXiv1209.0640OpenAlexW2614956027WikidataQ122971719 ScholiaQ122971719MaRDI QIDQ1784169

Ishai Dan-Cohen, Stefan Wewers, Jennifer S. Balakrishnan, Minhyong Kim

Publication date: 26 September 2018

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0640

zbMATH Keywords

hyperbolic curvesintegral points on curves

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Elliptic curves (14H52) Heights (11G50) Homotopy theory and fundamental groups in algebraic geometry (14F35)

Related Items (20)

"Equation missing" -Integral Points on a Mordell Curve ⋮ Quadratic Chabauty: \(p\)-adic heights and integral points on hyperelliptic curves ⋮ Quadratic Chabauty for modular curves: algorithms and examples ⋮ M_{0, 5}: Toward the Chabauty–Kim method in higher dimensions ⋮ Local constancy of pro‐unipotent Kummer maps ⋮ Weight filtrations on Selmer schemes and the effective Chabauty–Kim method ⋮ Mixed Tate motives and the unit equation. II ⋮ A note on abelian arithmetic BF‐theory ⋮ Reverse engineered Diophantine equations ⋮ Refined Selmer equations for the thrice-punctured line in depth two ⋮ Rational motivic path spaces and Kim's relative unipotent Section conjecture ⋮ Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture ⋮ Quadratic Chabauty and rational points. I: \(p\)-adic heights ⋮ Quadratic Chabauty for modular curves and modular forms of rank one ⋮ Morphisms of rational motivic homotopy types ⋮ Explicit quadratic Chabauty over number fields ⋮ The polylog quotient and the Goncharov quotient in computational Chabauty–Kim Theory I ⋮ Explicit Chabauty-Kim for the split Cartan modular curve of level 13 ⋮ Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture ⋮ Diophantine Geometry and Non-abelian Reciprocity Laws I

Uses Software

• GitHub

Cites Work

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