Speaker: Vijay Sookdeo, Catholic University

Title: Integral point in orbits of morphisms on curves

Abstract: Let f be a morphism on a curve C, both defined over a number field K. The forward orbit of a point P on C under f is the collection of all images P, f(P), f(f(P)), etc.; the backward orbit P under f is the collection of all pre-images of P. A theorem of J. Silverman gives a condition for when the forward orbit of P contains at most finitely many points with integral coordinates. We will introduce a conjecture for when the backward orbit of P contains at most finitely many integral points, and discuss results towards this conjecture.

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