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arXiv · 1406.0120

Heights and regulators of number fields and elliptic curves

Fabien Pazuki
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Abstract

We compare general inequalities between invariants of number fields and invariants of abelian varieties over number fields. On the number field side, we remark that there is only a finite number of non-CM number fields with bounded regulator. On the abelian side, assuming the height conjecture of Lang and Silverman, we obtain a Northcott property for the regulator on the set of abelian varieties with dense rational points over a number field. This amounts to say that the arithmetic of CM fields is similar, with respect to the invariants considered here, to the arithmetic of abelian varieties over a number field having a non Zariski dense Mordell-Weil group.

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Fabien Pazuki. 2016-10-06. Heights and regulators of number fields and elliptic curves. https://arxiv.org/abs/1406.0120

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