On finite orbits of infinite correspondences

TL;DR

This paper studies algebraic correspondences on projective lines, providing a field theoretic characterization of when such correspondences have finitely many finite orbits, thus advancing understanding of their dynamical properties.

Contribution

It offers a novel field theoretic criterion for determining the finiteness of finite orbits in algebraic correspondences on projective lines.

Findings

Characterization of finiteness of finite orbits using field theory

Extension of algebraic correspondence results to projective lines

Insights into the dynamics of algebraic correspondences

Abstract

These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic characterization of the (in)finiteness of the number of finite orbits.