Arithmetic Intersection Theory on Deligne-Mumford Stacks

TL;DR

This paper extends arithmetic intersection theory, including Chow groups and their product structures, from regular arithmetic varieties to regular Deligne-Mumford stacks over the integers of a number field.

Contribution

It introduces a framework for arithmetic intersection theory on Deligne-Mumford stacks, broadening the scope beyond traditional varieties.

Findings

Extended arithmetic Chow groups to stacks

Defined product structures on these groups

Established foundational properties for stacks over number fields

Abstract

The arithmetic Chow groups and their product structure are extended from the category of regular arithmetic varieties to regular Deligne-Mumford stacks over the ring of integers in a number field.