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- W4299570279 abstract "We lower bound the Faltings height of an abelian variety over a number field by the sum of its injectivity diameter and the norm of its bad reduction primes. It leads to an unconditional bound on the rank of Mordell-Weil groups. Assuming the height conjecture of Lang and Silverman, we then obtain a Northcott property for the regulator on the set of simple abelian varieties defined over a fixed number field, of fixed dimension $g$, bounded rank and with dense rational points over a number field. We remove the simplicity assumption in the principally polarized case by giving a refined version of the Lang-Silverman conjecture." @default.
- W4299570279 created "2022-10-02" @default.
- W4299570279 creator A5063289117 @default.
- W4299570279 date "2015-06-16" @default.
- W4299570279 modified "2023-09-26" @default.
- W4299570279 title "Heights, ranks and regulators of abelian varieties" @default.
- W4299570279 doi "https://doi.org/10.48550/arxiv.1506.05165" @default.
- W4299570279 hasPublicationYear "2015" @default.
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