Samenvatting
For an elliptic surface π:X→P1 defined over a number field K, a theorem of Silverman shows that for all but finitely many fibres above K-rational points, the resulting elliptic curve over K has Mordell-Weil rank at least as large as the rank of the group of sections of π. When X is a K3 surface with two distinct elliptic fibrations, we show that the set of K-rational points of P1 for which this rank inequality is strict, is not a thin set, under certain hypothesis on the fibrations. Our results provide one of the first cases of this phenomenon beyond that of rational elliptic surfaces.
Originele taal-2 | English |
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Pagina's (van-tot) | 771-781 |
Aantal pagina's | 11 |
Tijdschrift | Manuscripta mathematica |
Volume | 175 |
Vroegere onlinedatum | 28-jun.-2024 |
DOI's | |
Status | Published - nov.-2024 |