A note on Zilber-Pink in $Y(1)^n$

TL;DR

This paper proves two Zilber-Pink-type statements in the n-dimensional modular variety Y(1)^n, assuming a weak Lang-Trotter conjecture for pairs of elliptic curves, advancing understanding of unlikely intersections.

Contribution

It introduces new Zilber-Pink results in Y(1)^n under a conjectural assumption, extending prior work in unlikely intersection theory.

Findings

Proves two Zilber-Pink-type statements in Y(1)^n

Assumes a weak Lang-Trotter conjecture for pairs of elliptic curves

Builds on previous results to advance unlikely intersection theory

Abstract

Building on \cite{daworrpap,dawpap}, we prove two Zilber-Pink-type statements in $Y(1)^n$, assuming a weak form of the Lang-Trotter conjecture for pairs of elliptic curves.