ﻻ يوجد ملخص باللغة العربية
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.
We construct a functor from the smooth 4-dimensional manifolds to the hyper-algebraic number fields, i.e. fields with non-commutative multiplication. It is proved that that the simply connected 4-manifolds correspond to the abelian extensions. We rec
Recent important and powerful frameworks for the study of differential forms by Huber-Joerder and Huber-Kebekus-Kelly based on Voevodskys h-topology have greatly simplified and unified many approaches. This article builds towards the goal of putting
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from $p$-adic
We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and for the l
This is an English translation of Nikolai Chebotaryovs paper Die Probleme der modernen Galoisschen Theorie from 1932. An excerpt from this paper was given as a lecture at the International Congress of Mathematicians in Zurich in 1932. With the lectur