Problems in Arithmetic Topology

TL;DR

This paper compiles a diverse set of open problems in arithmetic topology discussed during a 2019 workshop, aiming to guide future research across various interconnected mathematical areas.

Contribution

It presents a curated list of open questions across three categories, reflecting the current challenges and directions in arithmetic topology.

Findings

Identified key open problems in topological analogues of arithmetic phenomena.

Highlighted challenges in point counts and stability phenomena.

Outlined tools and methods relevant to advancing the field.

Abstract

We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on "Arithmetic Topology". Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and engaged in shared discussions from their own perspectives as working mathematicians across various fields of study. Participants were explicitly asked to provide problems of various levels of difficulty, with the goal of capturing a cross-section of exciting challenges in the field that could help guide future activity. The problems, together with references and brief discussions when appropriate, are collected below into three categories: 1) topological analogues of arithmetic phenomena, 2) point counts, stability phenomena and the Grothendieck ring, and 3) tools, methods and examples.