Explicit height bounds for K-rational points on
transverse curves in powers of elliptic curves

Veneziano, Francesco; Viada, Evelina

doi:10.2140/pjm.2021.315.477

Pacific J. Math.

2021

DOI: 10.2140/pjm.2021.315.477

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Explicit height bounds for K-rational points on transverse curves in powers of elliptic curves

Francesco Veneziano

Evelina Viada

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Recent developments of the Uniform Mordell-Lang Conjecture

Gao¹

2021

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This expository survey is based on my online talk at the ICCM 2020. It aims to sketch key steps of the recent proof of the uniform Mordell-Lang conjecture for curves embedded into Jacobians (a question of Mazur). The full version of this conjecture is proved by combining Dimitrov-Gao-Habegger [DGH20b] and Kühne [Küh21a]. We include in this survey a detailed proof on how to combine these two results, which was implicitly done in [DGH20a] but not explicitly written in existing literature. At the end of the survey we state some future aspects.[1] When the number field F is fixed, [CHM97, CHM21] proved more: Assuming the widely open Strong Lang Conjecture, the cardinality #C(F ) is bounded above solely in terms of g except for finitely many F -isomorphic classes of curves C of genus g ≥ 2.

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Recent developments of the Uniform Mordell-Lang Conjecture

Gao¹

2021

Preprint

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Explicit height bounds for K-rational points on transverse curves in powers of elliptic curves

Cited by 1 publication

References 19 publications

Recent developments of the Uniform Mordell-Lang Conjecture

Recent developments of the Uniform Mordell-Lang Conjecture

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