• Corpus ID: 118546075

Heights, ranks and regulators of abelian varieties

  title={Heights, ranks and regulators of abelian varieties},
  author={Fabien Pazuki},
  journal={arXiv: Number Theory},
  • F. Pazuki
  • Published 16 June 2015
  • Mathematics
  • arXiv: Number Theory
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… 

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