Heights and Preperiodic Points of Polynomials over Function Fields

@inproceedings{Benedetto2008HeightsAP,
  title={Heights and Preperiodic Points of Polynomials over Function Fields},
  author={Robert L. Benedetto},
  year={2008}
}
Let K be a function field in one variable over an arbitrary field F. Given a rational function φ ∈ K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic points of φ all have canonical height zero; conversely, if F is a finite field, then every point of canonical height zero is preperiodic. However, if F is an infinite field, then there may be non-preperiodic points of canonical height zero. In this paper, we show… CONTINUE READING