Heights and preperiodic points of polynomials over function fields
| dc.creator | Benedetto, Robert L. | |
| dc.date | 2005-10-20 | |
| dc.date | 2005-12-13 | |
| dc.date.accessioned | 2026-07-07T06:47:43Z | |
| dc.date.available | 2026-07-07T06:47:43Z | |
| dc.description | Let K be a function field in one variable over an arbitrary field F. Given a rational function f(z) in 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 f 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 that for polynomial f, such points exist only if f is isotrivial. In fact, such K-rational points exist only if f is defined over the constant field of K after a K-rational change of coordinates. | |
| dc.description | 9 pages; added references, corrected minor typos, updated definition of isotrivial for dynamical systems, added Proposition 5.1 to clarify the main proof | |
| dc.identifier | https://arxiv.org/abs/math/0510444 | |
| dc.identifier | http://arxiv.org/abs/math/0510444 | |
| dc.identifier | IMRN 2005:62, 3855-3866 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103750 | |
| dc.subject | Number Theory | |
| dc.subject | Dynamical Systems | |
| dc.subject | 11G50 (Primary); 11D45, 37F10 (Secondary) | |
| dc.title | Heights and preperiodic points of polynomials over function fields | |
| dc.type | text |