On $\mathbb{Z}_p$-towers of graph coverings arising from a constant voltage assignment

TL;DR

This paper studies special $Z_p$-towers of graph coverings generated by constant voltage assignments, proving their uniqueness and analyzing their Iwasawa invariants, with applications to isogeny and volcano graph towers.

Contribution

It establishes the existence and uniqueness of $Z_p$-towers from constant voltage assignments and explores their Iwasawa invariants, extending to applications in isogeny and volcano graphs.

Findings

Proved the existence and uniqueness of $Z_p$-towers from constant voltage assignments.

Analyzed the Iwasawa invariants of these towers.

Applied results to towers of isogeny graphs and volcano graphs.

Abstract

We investigate properties of $\mathbb{Z}_p$-towers of graph coverings that arise from a constant voltage assignment. We prove the existence and uniqueness (up to isomorphisms) of such towers. Furthermore, we study the Iwasawa invariants of these towers, and apply our results to towers of isogeny graphs enhanced with level structures, as well as towers arising from volcano graphs.