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arXiv · 1506.05165

Heights, ranks and regulators of abelian varieties

Fabien Pazuki
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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.

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Fabien Pazuki. 2015-06-16. Heights, ranks and regulators of abelian varieties. https://arxiv.org/abs/1506.05165

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