On the properties of Northcott and Narkiewicz for elliptic curves
In this paper, as an analog of the number field case, for an elliptic curve E defined over the algebraic numbers and for any subfield F of algebraic numbers, we say that E has the Northcott property over F if there are at most finitely many F-rational points on E of uniformly bounded height, and we...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific
2022
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| Subjects: | |
| Online Access: | View Fulltext in Publisher |
| Summary: | In this paper, as an analog of the number field case, for an elliptic curve E defined over the algebraic numbers and for any subfield F of algebraic numbers, we say that E has the Northcott property over F if there are at most finitely many F-rational points on E of uniformly bounded height, and we say that E has the property (P) over F if for any infinite subset S of F-rational points on E, f(S) = S for an F-endomorphism f of E implies that f is an automorphism. We establish some criteria for both properties and provide typical examples. We also show that the Northcott property implies the property (P), but the converse is not true. © 2022 World Scientific Publishing Company. |
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| ISBN: | 17930421 (ISSN) |
| DOI: | 10.1142/S1793042122501081 |