Heights and regulators
PAZUKI, Fabien
Université Sciences et Technologies - Bordeaux 1 [UB]
Institut de Mathématiques de Bordeaux [IMB]
Université Sciences et Technologies - Bordeaux 1 [UB]
Institut de Mathématiques de Bordeaux [IMB]
PAZUKI, Fabien
Université Sciences et Technologies - Bordeaux 1 [UB]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Université Sciences et Technologies - Bordeaux 1 [UB]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Document de travail - Pré-publication
English 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 ...Read more >
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.Read less <
Origin
Hal imported