Stacky heights on elliptic curves in characteristic 3

TL;DR

This paper proves that in characteristic 3, the moduli stack of stable elliptic curves does not admit stacky heights that correspond to the classical Faltings height, resolving a question in the field.

Contribution

It demonstrates the non-existence of certain stacky heights in characteristic 3, providing a negative answer to a previously open question.

Findings

No stacky heights induce the Faltings height in characteristic 3

Addresses a question posed by Ellenberg, Satriano, and Zureick-Brown

Clarifies the behavior of heights on moduli stacks in characteristic 3

Abstract

We show there are no stacky heights on the moduli stack of stable elliptic curves in characteristic $3$ which induce the usual Faltings height, negatively answering a question of Ellenberg, Satriano, and Zureick-Brown.