Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem

TL;DR

This paper extends classical number theory theorems to algebraic stacks, proving finiteness and integral points results, and applies these to surfaces of general type.

Contribution

It introduces an analogue of Hermite-Minkowski's theorem and a Chevalley-Weil theorem for stacks, advancing the understanding of arithmetic properties of stacks.

Findings

Proved a stacky version of Hermite-Minkowski's finiteness theorem.

Established a Chevalley-Weil type theorem for integral points on stacks.

Derived analogues of the Shafarevich conjecture for certain surfaces of general type.

Abstract

We prove an analogue for algebraic stacks of Hermite-Minkowski's finiteness theorem from algebraic number theory, and establish a Chevalley-Weil type theorem for integral points on stacks. As an application of our results, we prove analogues of the Shafarevich conjecture for some surfaces of general type.