A topology on points on stacks

For a variety over certain topological rings R, like Z[subscript p] or C, there is a well-studied way to topologize the R-points on the variety. In this paper, we generalize this definition to algebraic stacks. For an algebraic stack X over many topological rings R, we define a topology on the isomorphism classes of R-points of X. We prove expected properties of the resulting topological spaces including functoriality. Then, we extend the definition to the case when R is the ring of adeles of some global field. Finally, we use this last definition to strengthen the local-global compatibility for stacky curves of Bhargava-Poonen to a strong approximation result.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2020

Author dc:creator

• Christensen, Atticus(Atticus Ballroom)

Advisor dc:contributor.advisor

• Bjorn Poonen.

• Mathematics.

Statement dc:rights

• MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/126918

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/126918