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.

我们提出了在2019年6月的PIMS / NSF研讨会上关于“算术拓扑”的算术拓扑问题列表。研讨会期间举办了三场问题会议，参与者作为听众在各个研究领域中的数学家，向听众提出了开放性问题，并从他们自己的角度进行了共同的讨论。明确要求参与者提供各种难度的问题，目的是捕获该领域令人兴奋的挑战的各个方面，以帮助指导未来的活动。这些问题，以及适当时的参考文献和简短讨论，分为以下三类：（1）算术现象的拓扑类似物；（2）点数，稳定性现象和Grothendieck环；以及（3）工具，方法和示例。