Problems in arithmetic topology
Problems in arithmetic topology
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DOI：
10.1007/s40687-021-00264-5
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发表时间：
2020-12
影响因子：
1.2
通讯作者：
Claudio Gómez-Gonzáles;J. Wolfson
中科院分区：
文献类型：
--
作者：
Claudio Gómez-Gonzáles;J. Wolfson
我们列出了 2019 年 6 月 PIMS/NSF 研讨会“算术拓扑”中提出的算术拓扑问题。研讨会期间举办了三场问题会议，参与者向观众提出了开放性问题，并从自己作为各个研究领域的工作数学家的角度进行了共同讨论。明确要求参与者提供各种难度级别的问题，目的是捕捉该领域令人兴奋的挑战的横截面，以帮助指导未来的活动。这些问题以及适当的参考文献和简短讨论被分为以下三类：（1）算术现象的拓扑类似物，（2）点数、稳定性现象和格罗腾迪克环，以及（3）工具、方法和示例。
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.