Rational points in periodic analytic sets and the Manin-Mumford conjecture

@article{Pila2008RationalPI,
  title={Rational points in periodic analytic sets and the Manin-Mumford conjecture},
  author={J. Pila and U. Zannier},
  journal={arXiv: Number Theory},
  year={2008}
}
We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to view torsion points as rational points on a complex torus and then compare (i) upper bounds for the number of rational points on a transcendental analytic variety (Bombieri-Pila-Wilkie) and (ii) lower bounds for the degree of a torsion point (Masser), after taking conjugates. In order to be able to deal with (i), we… Expand
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