On finite orbits of infinite correspondences

2025/11/10 by Manfred Buchacher, Buchacher, Manfred · 1 citation
Mathematics · #Finite Group Theory Research #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2511.07172

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.

Citations

• Separated Variables on Plane Algebraic Curves
• Separating Variables in Bivariate Polynomial Ideals: the Local Case
• On Differentially Algebraic Generating Series for Walks in the Quarter\n Plane
• Separating Variables in Bivariate Polynomial Ideals
• p-adic uniformization and the action of Galois on certain affine correspondences
• Critical dynamics of variable-separated affine correspondences
• Canonical heights for correspondences

Cited by

• x(1-t(x+x^-1))F(x;t) = x-tF(0;t)

Related

• Correspondence functors and finiteness conditions
• The representation theory of finite sets and correspondences
• Upper Bounds on the Sizes of Finite Orbits for Unramified Morphisms
• Orbits of automorphism groups of fields
• Scarcity of finite orbits for rational functions over a number field