A topology on points on stacks
Name
1191254024-MIT.pdf
Size
499.62 KB
Format
Adobe PDF
Checksum (MD5)
8ec0fa1753179279a5a7db035d9fa70c
Author(s)
Christensen, Atticus(Atticus Ballroom)
Advisor(s)
Bjorn Poonen.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (page 55).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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