CNRS Poncelet

Conference "Global Fields"

October 25 - 28, 2011

Moscow, Russia

RAS Poncelet

Organisers: Philippe Lebacque (Laboratoire de Mathématiques de Besançon ), Michael Tsfasman (CNRS, Laboratoire Poncelet, Institute for Information Transmission Problems), Alexey Zykin (Laboratoire Poncelet, State University Higher School of Economics, IITP)

Iteration of algebraic points under a rational self-map

Ekaterina Amerik (Moscow)

Friday 28 October, 12:00 - 13:30

Abstract

Let $X$ be an algebraic variety and $f$ a dominant rational self-map of $X$, both defined over a number field. We shall study Zariski closures of iterated orbits $\{f^k(x), k\geq 0}$, where $x$ is an algebraic point of $X$. In particular we shall show that any such self-map of infinite order admits a non-preperiodic algebraic point. In the same spirit, a conjecture of Zhang affirms that a regular polarized self-map should have an algebraic point with Zariski-dense iterated orbit. If time permits, we shall make some (starting) remarks concerning this conjecture for surfaces.

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