Konferenz: Symposium about Pure Mathematics


Canonical heights in arithmetic dynamical systems

{{_Ltalk:R}} Dr. Patrick Ingram
Datum: 09.12.10   Zeit: 13.30 - 14.30   Raum: Y27H12

Abstract: To every rational function defined over a number field, one can associate a canonical height function which carries information about the arithmetic information of the function under iteration. These canonical heights are natural generalizations of Green's functions (in the context of complex dynamical systems) and Néron- Tate heights (in the context of abelian varieties). We will survey some of what is known about these canonical heights, with an emphasis on analogies with the properties of elliptic curves.