Arithmetic McKay correspondence

TL;DR

This paper introduces an arithmetic version of the McKay correspondence, linking zeta functions of certain Deligne-Mumford stacks with those of their crepant resolutions, supported by illustrative examples.

Contribution

It establishes a novel arithmetic McKay correspondence connecting zeta functions of stacks and resolutions, expanding the classical geometric correspondence into an arithmetic context.

Findings

Zeta functions of Deligne-Mumford stacks relate to those of crepant resolutions.

Examples demonstrate the correspondence in specific cases.

The framework broadens understanding of arithmetic geometry and stack resolutions.

Abstract

We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some examples are discussed.