The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations

Abstract

We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus $g\in [2/3,1)$ that are defined using generalized Fermat equations, extending a result of Darmon and Granville. We then apply our methods to find that a positive proportion of curves in our family satisfy the integral Hasse principle.

41 pages