Bounding periods of subvarieties of $(\mathbb{P}^1)^n$

Abstract

Using methods of p-adic analysis, along with the powerful result of Medvedev-Scanlon [MS14] for the classification of periodic subvarieties of (P 1 ) n , we bound the length of the orbit of a periodic subvariety Y ⊂ (P 1 ) n under the action of a dominant endomorphism.

Rational self-maps with a regular iterate on a semiabelian variety

“…Invariant subvarieties appear naturally in the main conjectures in arithmetic dynamics, such as the Dynamical Mordell-Lang Conjecture (see [BGT16]) and the Dynamical Manin-Mumford Conjecture (see [GTZ11,GT21]). Totally invariant subvarieties come up in the study of the algebraic degree of a self-map Ψ : G → G (see [BG]) and are related to arithmetic properties of Ψ; see [Can10,BGT15a,BGT19].…”