{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/126918"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/126918","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A topology on points on stacks","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.","abstract_html":"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. 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