Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties

DOI10.1093/imrn/rnz362OpenAlexW3004082426WikidataQ126629539 ScholiaQ126629539MaRDI QIDQ5068201

Jennifer S. Balakrishnan, Netan Dogra

Publication date: 5 April 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.00401

Mathematics Subject Classification ID

Rational points (14G05) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (13)

Geometric quadratic Chabauty over number fields ⋮ Quadratic Chabauty and 𝑝-adic Gross–Zagier ⋮ A geometric linear Chabauty comparison theorem ⋮ Explicit Vologodsky integration for hyperelliptic curves ⋮ Quadratic Chabauty for modular curves: algorithms and examples ⋮ A Chabauty-Coleman bound for surfaces ⋮ Geometric quadratic Chabauty and \(p\)-adic heights ⋮ Rational points on \(X_0^+(125)\) ⋮ Quadratic Chabauty for Atkin–Lehner quotients of modular curves of prime level and genus 4, 5, 6 ⋮ Explicit methods in number theory. Abstracts from the workshop held July 18--24, 2021 (hybrid meeting) ⋮ An effective Chabauty–Kim theorem ⋮ Quadratic Chabauty for modular curves and modular forms of rank one ⋮ Diagonal genus 5 curves, elliptic curves over $\mathbb {Q}(t)$, and rational diophantine quintuples

Uses Software

• Magma
• SageMath
• GitHub
• QCI

Cites Work

• Deformations of polarized automorphic Galois representations and adjoint Selmer groups
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• Hodge cycles, motives, and Shimura varieties
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• A finiteness theorem for the symmetric square of an elliptic curve
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• The \(\ell\)-component of the unipotent Albanese map
• Elliptic curves over real quadratic fields are modular
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• The motivic fundamental group of \(\mathbf P^1\setminus\{0,1,\infty\}\) and the theorem of Siegel
• Appendix and erratum to “Massey products for elliptic curves of rank 1”
• Towards non–abelian 𝑝–adic Hodge theory in the good reduction case
• Massey products for elliptic curves of rank 1
• Relative Weight Filtrations on Completions of Mapping Class Groups
• The Hasse Principle modulo nth powers
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• Coleman integration for even-degree models of hyperelliptic curves
• SOME SPECIAL FAMILIES OF HYPERELLIPTIC CURVES
• GALOIS ACTIONS ON FUNDAMENTAL GROUPS OF CURVES AND THE CYCLE $C-C^{-}$
• THEp-TORSION OF ELLIPTIC CURVES IS UNIFORMLY BOUNDED
• Modeles de neron et monodromie
• De Rham cohomology of differential modules on algebraic varieties
• Coleman integration using the Tannakian formalism
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