On a Problem of Lang for Matrix Polynomials

TL;DR

This paper explores a problem posed by Lang regarding the finiteness of torsion points on plane rational curves over complex numbers, extending the discussion to a matrix analogue.

Contribution

It introduces a matrix analogue of Lang's problem and provides initial results towards understanding torsion points in this new context.

Findings

Results towards finiteness of torsion points in matrix setting

Extension of Lang's problem to matrices over complex numbers

Initial theoretical insights into matrix analogues of rational curves

Abstract

In this paper, we consider a problem of Lang about finiteness of torsion points on plane rational curves over $\mathbb C$, and prove some results towards a matrix analogue of this problem.