Stacky heights on elliptic curves 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.

arXiv commentI have made significant changes and restructured the argument based on a number of suggestions and corrections from an anonymous referee