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Explicit height
bounds for $K$-rational points on transverse curves in powers
of elliptic curves
Francesco Veneziano and Evelina Viada |
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Vol. 315 (2021), No. 2, 477–503
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DOI: 10.2140/pjm.2021.315.477
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Abstract |
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Let be an algebraic curve embedded transversally in a power of an elliptic curve with complex multiplication. We produce a good explicit bound for the height of all the algebraic points on contained in the union of all proper algebraic subgroups of . The method gives a totally explicit version of the Manin–Demjanenko theorem in the elliptic case and complements previous results only proved when does not have complex multiplication. |
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Keywords
Mordell conjecture, subvarieties of products of elliptic
curves, diophantine approximation
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Mathematical Subject Classification
Primary: 11G50, 14G40
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Milestones
Received: 16 June 2020
Revised: 6 September 2021
Accepted: 6 September 2021
Published: 19 January 2022
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Authors |
| Francesco Veneziano | |
| Dipartimento di matematica Università degli Studi di Genova 16146 Genova (GE) Italy |
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| Evelina Viada | |
| Mathematisches Institut Georg-August-Universität D-37073 Göttingen Germany |
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