Year: 2026
Type: preprint
Abstract: Levin asked what can be said about the locus of points lying on a given curve in $\mathbb{G}_m^n$ that have a non-zero integer power on another given curve in $\mathbb{G}_m^n$ for $n \geq 3$. We give a definite answer to the abelian analog of Levin's question, proving what is predicted by the Zilber-Pink conjecture in this case. An important ingredient in our proof is a strengthening of a height inequality by Vojta and Rémond.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221047106